(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 13.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 93301, 2602] NotebookOptionsPosition[ 87431, 2515] NotebookOutlinePosition[ 87912, 2534] CellTagsIndexPosition[ 87869, 2531] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Numerical data", "Section",ExpressionUUID->"a68e1e90-2158-4da8-9829-76467decd8c9"], Cell[BoxData[ RowBox[{ RowBox[{"\[Epsilon]4", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1.0", ",", "23.284472"}], "}"}], ",", RowBox[{"{", RowBox[{"1.025", ",", "23.540448"}], "}"}], ",", RowBox[{"{", RowBox[{"1.05", ",", "23.781121"}], "}"}], ",", RowBox[{"{", RowBox[{"1.075", ",", "24.002084"}], "}"}], ",", RowBox[{"{", RowBox[{"1.1", ",", "24.196931"}], "}"}], ",", RowBox[{"{", RowBox[{"1.125", ",", "24.355758"}], "}"}], ",", RowBox[{"{", RowBox[{"1.15", ",", "24.463104"}], "}"}], ",", RowBox[{"{", RowBox[{"1.175", ",", "24.497569"}], "}"}], ",", RowBox[{"{", RowBox[{"1.2", ",", "24.439877"}], "}"}], ",", RowBox[{"{", RowBox[{"1.225", ",", "24.289859"}], "}"}], ",", RowBox[{"{", RowBox[{"1.25", ",", "24.069414"}], "}"}], ",", RowBox[{"{", RowBox[{"1.275", ",", "23.805244"}], "}"}], ",", RowBox[{"{", RowBox[{"1.3", ",", "23.516919"}], "}"}], ",", RowBox[{"{", RowBox[{"1.325", ",", "23.216331"}], "}"}], ",", RowBox[{"{", RowBox[{"1.35", ",", "22.910393"}], "}"}]}], "}"}]}], ";"}]], "Input",Ex\ pressionUUID->"682f75fb-1edd-4aa6-a4ad-b597c5f869c9"], Cell[BoxData[ RowBox[{ RowBox[{"\[Epsilon]5", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1.1", ",", "27.103397"}], "}"}], ",", RowBox[{"{", RowBox[{"1.125", ",", "26.784466"}], "}"}], ",", RowBox[{"{", RowBox[{"1.15", ",", "26.509573"}], "}"}], ",", RowBox[{"{", RowBox[{"1.175", ",", "26.299399"}], "}"}], ",", RowBox[{"{", RowBox[{"1.2", ",", "26.172614"}], "}"}], ",", RowBox[{"{", RowBox[{"1.225", ",", "26.128902"}], "}"}], ",", RowBox[{"{", RowBox[{"1.25", ",", "26.146006"}], "}"}], ",", RowBox[{"{", RowBox[{"1.275", ",", "26.197002"}], "}"}], ",", RowBox[{"{", RowBox[{"1.3", ",", "26.262232"}], "}"}], ",", RowBox[{"{", RowBox[{"1.325", ",", "26.329847"}], "}"}], ",", RowBox[{"{", RowBox[{"1.35", ",", "26.393103"}], "}"}]}], "}"}]}], ";"}]], "Input", CellLabel->"In[14]:=",ExpressionUUID->"35c12977-2872-4eab-be4f-329f455172b3"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Epsilon]4", ",", "\[Epsilon]5"}], "}"}], ",", RowBox[{"PlotTheme", "\[Rule]", "\"\\""}], ",", RowBox[{"Joined", "\[Rule]", "True"}]}], "]"}]], "Input", CellLabel->"In[15]:=",ExpressionUUID->"59810817-5144-4818-800a-a2ceb8fcd500"], Cell[BoxData[ GraphicsBox[{{}, {{}, {}, {RGBColor[0.790588, 0.201176, 0.], PointSize[0.012833333333333334`], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1., 23.284472}, {1.025, 23.540448}, {1.05, 23.781121}, {1.075, 24.002084}, {1.1, 24.196931}, {1.125, 24.355758}, {1.15, 24.463104}, { 1.175, 24.497569}, {1.2, 24.439877}, {1.225, 24.289859}, {1.25, 24.069414}, {1.275, 23.805244}, {1.3, 23.516919}, {1.325, 23.216331}, { 1.35, 22.910393}}]}, {RGBColor[0.192157, 0.388235, 0.807843], PointSize[0.012833333333333334`], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1.1, 27.103397}, {1.125, 26.784466}, {1.15, 26.509573}, {1.175, 26.299399}, {1.2, 26.172614}, {1.225, 26.128902}, {1.25, 26.146006}, { 1.275, 26.197002}, {1.3, 26.262232}, {1.325, 26.329847}, {1.35, 26.393103}}]}}, {{}, {}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{False, False}, AxesLabel->{None, None}, AxesOrigin->{0.9927083333333359, 22.677448333333384`}, DisplayFunction->Identity, Frame->{{True, False}, {True, False}}, FrameLabel->{{None, None}, {None, None}}, FrameStyle->{{ StrokeForm[ Opacity[0]], StrokeForm[ Opacity[0]]}, {Automatic, None}}, FrameTicks->FrontEndValueCache[{{Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}]& , None}, { Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}]& , None}}, {{{{23., FormBox["23", TraditionalForm], {0.01, 0.}}, {24., FormBox["24", TraditionalForm], {0.01, 0.}}, {25., FormBox["25", TraditionalForm], {0.01, 0.}}, {26., FormBox["26", TraditionalForm], {0.01, 0.}}, {27., FormBox["27", TraditionalForm], {0.01, 0.}}}, None}, {{{1., FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.0\"", ShowStringCharacters -> False], 1.`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.1, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.1\"", ShowStringCharacters -> False], 1.1`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.2, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.2\"", ShowStringCharacters -> False], 1.2`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.3, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.3\"", ShowStringCharacters -> False], 1.3`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}}, None}}], GridLines->{None, None}, GridLinesStyle->Directive[ GrayLevel[0.4, 0.5], AbsoluteThickness[1], AbsoluteDashing[{1, 2}]], Method->{ "OptimizePlotMarkers" -> True, "OptimizePlotMarkers" -> True, "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ Identity[ Part[#, 1]], Identity[ Part[#, 2]]}& ), "CopiedValueFunction" -> ({ Identity[ Part[#, 1]], Identity[ Part[#, 2]]}& )}}, PlotRange->{{0.9927083333333359, 1.35}, {22.677448333333384`, 27.103397}}, PlotRangeClipping->True, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.05], Scaled[0.05]}}, Ticks->{Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}, RotateLabel -> 0]& , Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}, RotateLabel -> 0]& }]], "Output",\ CellLabel->"Out[15]=",ExpressionUUID->"814e3769-9eaf-4e1a-8956-617c8e61d77e"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"Z4", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1.0", ",", "0.964721"}], "}"}], ",", RowBox[{"{", RowBox[{"1.025", ",", "0.961772"}], "}"}], ",", RowBox[{"{", RowBox[{"1.05", ",", "0.956999"}], "}"}], ",", RowBox[{"{", RowBox[{"1.075", ",", "0.948699"}], "}"}], ",", RowBox[{"{", RowBox[{"1.1", ",", "0.933404"}], "}"}], ",", RowBox[{"{", RowBox[{"1.125", ",", "0.904167"}], "}"}], ",", RowBox[{"{", RowBox[{"1.15", ",", "0.848555"}], "}"}], ",", RowBox[{"{", RowBox[{"1.175", ",", "0.751875"}], "}"}], ",", RowBox[{"{", RowBox[{"1.2", ",", "0.616552"}], "}"}], ",", RowBox[{"{", RowBox[{"1.225", ",", "0.476710"}], "}"}], ",", RowBox[{"{", RowBox[{"1.25", ",", "0.365270"}], "}"}], ",", RowBox[{"{", RowBox[{"1.275", ",", "0.287739"}], "}"}], ",", RowBox[{"{", RowBox[{"1.3", ",", "0.235707"}], "}"}], ",", RowBox[{"{", RowBox[{"1.325", ",", "0.200378"}], "}"}], ",", RowBox[{"{", RowBox[{"1.35", ",", "0.175725"}], "}"}]}], "}"}]}], ";"}]], "Input", CellLabel->"In[18]:=",ExpressionUUID->"5f735bd6-ba1a-4987-b9f7-8ff4ac674345"], Cell[BoxData[ RowBox[{ RowBox[{"Z5", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1.1", ",", "0.021813"}], "}"}], ",", RowBox[{"{", RowBox[{"1.125", ",", "0.048282"}], "}"}], ",", RowBox[{"{", RowBox[{"1.15", ",", "0.100987"}], "}"}], ",", RowBox[{"{", RowBox[{"1.175", ",", "0.194635"}], "}"}], ",", RowBox[{"{", RowBox[{"1.2", ",", "0.326815"}], "}"}], ",", RowBox[{"{", RowBox[{"1.225", ",", "0.463419"}], "}"}], ",", RowBox[{"{", RowBox[{"1.25", ",", "0.571546"}], "}"}], ",", RowBox[{"{", RowBox[{"1.275", ",", "0.645708"}], "}"}], ",", RowBox[{"{", RowBox[{"1.3", ",", "0.694337"}], "}"}], ",", RowBox[{"{", RowBox[{"1.325", ",", "0.726254"}], "}"}], ",", RowBox[{"{", RowBox[{"1.35", ",", "0.747506"}], "}"}]}], "}"}]}], ";"}]], "Input", CellLabel->"In[19]:=",ExpressionUUID->"5928cf25-152d-4cb2-9ce3-3f99ce9557d3"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"{", RowBox[{"Z4", ",", "Z5"}], "}"}], ",", RowBox[{"PlotTheme", "\[Rule]", "\"\\""}], ",", RowBox[{"Joined", "\[Rule]", "True"}]}], "]"}]], "Input", CellLabel->"In[20]:=",ExpressionUUID->"33a86cd9-4a3d-4b09-91de-2cbb886a6250"], Cell[BoxData[ GraphicsBox[{{}, {{}, {}, {RGBColor[0.790588, 0.201176, 0.], PointSize[0.012833333333333334`], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1., 0.964721}, {1.025, 0.961772}, {1.05, 0.956999}, {1.075, 0.948699}, {1.1, 0.933404}, {1.125, 0.904167}, {1.15, 0.848555}, {1.175, 0.751875}, {1.2, 0.616552}, {1.225, 0.47671}, {1.25, 0.36527}, {1.275, 0.287739}, {1.3, 0.235707}, {1.325, 0.200378}, {1.35, 0.175725}}]}, {RGBColor[0.192157, 0.388235, 0.807843], PointSize[0.012833333333333334`], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1.1, 0.021813}, {1.125, 0.048282}, {1.15, 0.100987}, {1.175, 0.194635}, {1.2, 0.326815}, {1.225, 0.463419}, {1.25, 0.571546}, {1.275, 0.645708}, {1.3, 0.694337}, {1.325, 0.726254}, {1.35, 0.747506}}]}}, {{}, {}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{False, False}, AxesLabel->{None, None}, AxesOrigin->{0.9927083333333359, 0}, DisplayFunction->Identity, Frame->{{True, False}, {True, False}}, FrameLabel->{{None, None}, {None, None}}, FrameStyle->{{ StrokeForm[ Opacity[0]], StrokeForm[ Opacity[0]]}, {Automatic, None}}, FrameTicks->FrontEndValueCache[{{Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}]& , None}, { Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}]& , None}}, {{{{0., FormBox["0", TraditionalForm], {0.01, 0.}}, {0.2, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"0.2\"", ShowStringCharacters -> False], 0.2`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 0.4, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"0.4\"", ShowStringCharacters -> False], 0.4`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 0.6, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"0.6\"", ShowStringCharacters -> False], 0.6`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 0.8, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"0.8\"", ShowStringCharacters -> False], 0.8`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, {1., FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.0\"", ShowStringCharacters -> False], 1.`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}}, None}, {{{1., FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.0\"", ShowStringCharacters -> False], 1.`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.1, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.1\"", ShowStringCharacters -> False], 1.1`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.2, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.2\"", ShowStringCharacters -> False], 1.2`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.3, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.3\"", ShowStringCharacters -> False], 1.3`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}}, None}}], GridLines->{None, None}, GridLinesStyle->Directive[ GrayLevel[0.4, 0.5], AbsoluteThickness[1], AbsoluteDashing[{1, 2}]], Method->{ "OptimizePlotMarkers" -> True, "OptimizePlotMarkers" -> True, "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ Identity[ Part[#, 1]], Identity[ Part[#, 2]]}& ), "CopiedValueFunction" -> ({ Identity[ Part[#, 1]], Identity[ Part[#, 2]]}& )}}, PlotRange->{{0.9927083333333359, 1.35}, {0, 0.964721}}, PlotRangeClipping->True, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.02], Scaled[0.05]}}, Ticks->{Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}, RotateLabel -> 0]& , Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}, RotateLabel -> 0]& }]], "Output",\ CellLabel->"Out[20]=",ExpressionUUID->"d32fbdb3-4ad8-4d05-aa55-4c32ff841fbc"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"ZZ4", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1.0", ",", "0.000259"}], "}"}], ",", RowBox[{"{", RowBox[{"1.025", ",", "0.001499"}], "}"}], ",", RowBox[{"{", RowBox[{"1.05", ",", "0.004661"}], "}"}], ",", RowBox[{"{", RowBox[{"1.075", ",", "0.011599"}], "}"}], ",", RowBox[{"{", RowBox[{"1.1", ",", "0.026034"}], "}"}], ",", RowBox[{"{", RowBox[{"1.125", ",", "0.055329"}], "}"}], ",", RowBox[{"{", RowBox[{"1.15", ",", "0.112492"}], "}"}], ",", RowBox[{"{", RowBox[{"1.175", ",", "0.212615"}], "}"}], ",", RowBox[{"{", RowBox[{"1.2", ",", "0.352622"}], "}"}], ",", RowBox[{"{", RowBox[{"1.225", ",", "0.496698"}], "}"}], ",", RowBox[{"{", RowBox[{"1.25", ",", "0.610946"}], "}"}], ",", RowBox[{"{", RowBox[{"1.275", ",", "0.690069"}], "}"}], ",", RowBox[{"{", RowBox[{"1.3", ",", "0.742975"}], "}"}], ",", RowBox[{"{", RowBox[{"1.325", ",", "0.778807"}], "}"}], ",", RowBox[{"{", RowBox[{"1.35", ",", "0.803778"}], "}"}]}], "}"}]}], ";"}]], "Input", CellLabel->"In[12]:=",ExpressionUUID->"051138e6-33b2-49e1-b570-b5e33fd33d7f"], Cell[BoxData[ RowBox[{ RowBox[{"ZZ5", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1.1", ",", "0.947557"}], "}"}], ",", RowBox[{"{", RowBox[{"1.125", ",", "0.917757"}], "}"}], ",", RowBox[{"{", RowBox[{"1.15", ",", "0.860133"}], "}"}], ",", RowBox[{"{", RowBox[{"1.175", ",", "0.759591"}], "}"}], ",", RowBox[{"{", RowBox[{"1.2", ",", "0.619206"}], "}"}], ",", RowBox[{"{", RowBox[{"1.225", ",", "0.474792"}], "}"}], ",", RowBox[{"{", RowBox[{"1.25", ",", "0.360243"}], "}"}], ",", RowBox[{"{", RowBox[{"1.275", ",", "0.280855"}], "}"}], ",", RowBox[{"{", RowBox[{"1.3", ",", "0.227717"}], "}"}], ",", RowBox[{"{", RowBox[{"1.325", ",", "0.191686"}], "}"}], ",", RowBox[{"{", RowBox[{"1.35", ",", "0.166547"}], "}"}]}], "}"}]}], ";"}]], "Input", CellLabel->"In[16]:=",ExpressionUUID->"37bd2bc4-e119-4f55-88d4-845984e63c22"], Cell[BoxData[ RowBox[{"(*", " ", RowBox[{ RowBox[{"(", "1", ")"}], " ", "\[Rule]", " ", RowBox[{"(", RowBox[{"2", ",", "2"}], ")"}]}], " ", "*)"}]], "Input",ExpressionUUID->\ "c2496421-c71c-4de1-a28d-dd9067951fda"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"{", RowBox[{"ZZ4", ",", "ZZ5"}], "}"}], ",", RowBox[{"PlotTheme", "\[Rule]", "\"\\""}], ",", RowBox[{"Joined", "\[Rule]", "True"}]}], "]"}]], "Input", CellLabel->"In[17]:=",ExpressionUUID->"bbbc4763-dda3-4da9-8ff0-9b7dc9932b23"], Cell[BoxData[ GraphicsBox[{{}, {{}, {}, {RGBColor[0.790588, 0.201176, 0.], PointSize[0.012833333333333334`], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1., 0.000259}, {1.025, 0.001499}, {1.05, 0.004661}, {1.075, 0.011599}, {1.1, 0.026034}, {1.125, 0.055329}, {1.15, 0.112492}, {1.175, 0.212615}, {1.2, 0.352622}, {1.225, 0.496698}, {1.25, 0.610946}, { 1.275, 0.690069}, {1.3, 0.742975}, {1.325, 0.778807}, {1.35, 0.803778}}]}, {RGBColor[0.192157, 0.388235, 0.807843], PointSize[0.012833333333333334`], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1.1, 0.947557}, {1.125, 0.917757}, {1.15, 0.860133}, {1.175, 0.759591}, {1.2, 0.619206}, {1.225, 0.474792}, {1.25, 0.360243}, {1.275, 0.280855}, {1.3, 0.227717}, {1.325, 0.191686}, {1.35, 0.166547}}]}}, {{}, {}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{False, False}, AxesLabel->{None, None}, AxesOrigin->{0.9927083333333359, 0}, DisplayFunction->Identity, Frame->{{True, False}, {True, False}}, FrameLabel->{{None, None}, {None, None}}, FrameStyle->{{ StrokeForm[ Opacity[0]], StrokeForm[ Opacity[0]]}, {Automatic, None}}, FrameTicks->FrontEndValueCache[{{Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}]& , None}, { Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}]& , None}}, {{{{0., FormBox["0", TraditionalForm], {0.01, 0.}}, {0.2, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"0.2\"", ShowStringCharacters -> False], 0.2`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 0.4, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"0.4\"", ShowStringCharacters -> False], 0.4`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 0.6, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"0.6\"", ShowStringCharacters -> False], 0.6`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 0.8, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"0.8\"", ShowStringCharacters -> False], 0.8`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}}, None}, {{{1., FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.0\"", ShowStringCharacters -> False], 1.`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.1, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.1\"", ShowStringCharacters -> False], 1.1`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.2, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.2\"", ShowStringCharacters -> False], 1.2`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.3, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.3\"", ShowStringCharacters -> False], 1.3`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}}, None}}], GridLines->{None, None}, GridLinesStyle->Directive[ GrayLevel[0.4, 0.5], AbsoluteThickness[1], AbsoluteDashing[{1, 2}]], Method->{ "OptimizePlotMarkers" -> True, "OptimizePlotMarkers" -> True, "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ Identity[ Part[#, 1]], Identity[ Part[#, 2]]}& ), "CopiedValueFunction" -> ({ Identity[ Part[#, 1]], Identity[ Part[#, 2]]}& )}}, PlotRange->{{0.9927083333333359, 1.35}, {0, 0.947557}}, PlotRangeClipping->True, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.02], Scaled[0.05]}}, Ticks->{Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}, RotateLabel -> 0]& , Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}, RotateLabel -> 0]& }]], "Output",\ CellLabel->"Out[17]=",ExpressionUUID->"cad1c286-e9fa-457d-9d0f-e5060da9432b"] }, Open ]], Cell[BoxData[{ RowBox[{ RowBox[{"eps", "=", RowBox[{"Import", "[", "\"\<~/Dropbox/quack/H2_6-31g_e_3.dat\>\"", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"epsZ", "=", RowBox[{"Import", "[", "\"\<~/Dropbox/quack/H2_6-31g_Z_3.dat\>\"", "]"}]}], ";"}]}], "Input", CellChangeTimes->{{3.851224781838089*^9, 3.8512248063112907`*^9}, 3.8512252162611103`*^9, {3.851225406389719*^9, 3.8512254135446*^9}}, CellLabel->"In[31]:=",ExpressionUUID->"c351c0eb-ffe9-41ea-b9a4-ee9c001a879d"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"eps", "\[LeftDoubleBracket]", RowBox[{"k", ",", "1"}], "\[RightDoubleBracket]"}], ",", RowBox[{"eps", "\[LeftDoubleBracket]", RowBox[{"k", ",", "n"}], "\[RightDoubleBracket]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"n", ",", "2", ",", "10"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", RowBox[{"Length", "[", "eps", "]"}]}], "}"}]}], "]"}], ",", RowBox[{"PlotTheme", "\[Rule]", "\"\\""}], ",", RowBox[{"Joined", "\[Rule]", "True"}]}], "]"}]], "Input", CellChangeTimes->{{3.85122480749051*^9, 3.851224864147612*^9}, { 3.851224940625348*^9, 3.851225002439535*^9}, {3.851225040451601*^9, 3.851225091883659*^9}, {3.851225124903017*^9, 3.851225125940886*^9}, { 3.851225330238618*^9, 3.851225355378878*^9}, {3.851225388992231*^9, 3.851225389155015*^9}}, CellLabel->"In[25]:=",ExpressionUUID->"3dc691e1-f05a-4c4c-8978-c337f01f76cf"], Cell[BoxData[ GraphicsBox[{{}, {{}, {}, {RGBColor[0.790588, 0.201176, 0.], PointSize[0.009166666666666668], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1., -67.071819}, {1.025, -66.241153}, {1.05, -65.450083}, { 1.075, -64.6967}, {1.1, -63.979235}, {1.125, -63.296047}, { 1.15, -62.645614}, {1.175, -62.026518}, {1.2, -61.43744}, { 1.225, -60.877141}, {1.25, -60.344459}, {1.275, -59.838294}, { 1.3, -59.357603}, {1.325, -58.901389}, {1.35, -58.468692}, { 1.375, -58.216274}, {1.4, -57.824379}}]}, {RGBColor[0.192157, 0.388235, 0.807843], PointSize[0.009166666666666668], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1., -58.623711}, {1.025, -58.563333}, {1.05, -58.504956}, { 1.075, -58.447203}, {1.1, -58.388713}, {1.125, -58.32816}, { 1.15, -58.264269}, {1.175, -58.195841}, {1.2, -58.121769}, { 1.225, -58.041055}, {1.25, -57.952826}, {1.275, -57.85634}, { 1.3, -57.750997}, {1.325, -57.636343}, {1.35, -57.512066}, { 1.375, -57.270398}, {1.4, -57.128207}}]}, {RGBColor[1., 0.607843, 0.], PointSize[0.009166666666666668], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1., -38.390529}, {1.025, -38.020108}, {1.05, -37.657111}, { 1.075, -37.301375}, {1.1, -36.952753}, {1.125, -36.611115}, { 1.15, -36.276346}, {1.175, -35.94834}, {1.2, -35.627002}, { 1.225, -35.312246}, {1.25, -35.003991}, {1.275, -34.70216}, { 1.3, -34.406679}, {1.325, -34.117473}, {1.35, -33.83447}, { 1.375, -33.641535}, {1.4, -33.37055}}]}, {RGBColor[0., 0.596078, 0.109804], PointSize[0.009166666666666668], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1., 23.284472}, {1.025, 23.540448}, {1.05, 23.781121}, {1.075, 24.002084}, {1.1, 24.196931}, {1.125, 24.355758}, {1.15, 24.463104}, { 1.175, 24.497569}, {1.2, 24.439877}, {1.225, 24.289859}, {1.25, 24.069414}, {1.275, 23.805244}, {1.3, 23.516919}, {1.325, 23.216331}, { 1.35, 22.910393}, {1.375, 23.258001}, {1.4, 22.954121}}]}, {RGBColor[0.567426, 0.32317, 0.729831], PointSize[0.009166666666666668], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1., 28.599216}, {1.025, 28.204056}, {1.05, 27.820422}, {1.075, 27.451719}, {1.1, 27.103397}, {1.125, 26.784466}, {1.15, 26.509573}, { 1.175, 26.299399}, {1.2, 26.172614}, {1.225, 26.128902}, {1.25, 26.146006}, {1.275, 26.197002}, {1.3, 26.262232}, {1.325, 26.329847}, { 1.35, 26.393103}, {1.375, 25.591742}, {1.4, 25.484738}}]}, {RGBColor[0., 0.588235, 0.705882], PointSize[0.009166666666666668], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1., 48.641983}, {1.025, 48.588177}, {1.05, 48.504272}, {1.075, 48.419204}, {1.1, 48.331931}, {1.125, 48.241414}, {1.15, 48.14664}, { 1.175, 48.046638}, {1.2, 47.940507}, {1.225, 47.827425}, {1.25, 47.706672}, {1.275, 47.577637}, {1.3, 47.439833}, {1.325, 47.292895}, { 1.35, 47.136588}, {1.375, 47.241166}, {1.4, 47.066894}}]}, {RGBColor[0.8505, 0.4275, 0.13185], PointSize[0.009166666666666668], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1., 48.671943}, {1.025, 48.750422}, {1.05, 48.854852}, {1.075, 48.953891}, {1.1, 49.0462}, {1.125, 49.130498}, {1.15, 49.205585}, { 1.175, 49.270359}, {1.2, 49.323832}, {1.225, 49.365142}, {1.25, 49.393571}, {1.275, 49.408547}, {1.3, 49.298772}, {1.325, 48.828426}, { 1.35, 48.380629}, {1.375, 47.758995}, {1.4, 47.337534}}]}, {RGBColor[0.499929, 0.285875, 0.775177], PointSize[0.009166666666666668], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1., 56.04421}, {1.025, 55.439455}, {1.05, 54.85986}, {1.075, 54.296173}, {1.1, 53.734711}, {1.125, 53.16163}, {1.15, 52.575077}, { 1.175, 51.986525}, {1.2, 51.408299}, {1.225, 50.847802}, {1.25, 50.308585}, {1.275, 49.792109}, {1.3, 49.40965}, {1.325, 49.396616}, { 1.35, 49.369333}, {1.375, 49.130262}, {1.4, 48.867172}}]}, {RGBColor[0.12490296143062507`, 0.63, 0.47103259454284074`], PointSize[ 0.009166666666666668], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1., 57.406912}, {1.025, 56.577538}, {1.05, 55.796352}, {1.075, 55.069086}, {1.1, 54.406125}, {1.125, 53.818231}, {1.15, 53.304366}, { 1.175, 52.850334}, {1.2, 52.441244}, {1.225, 52.06726}, {1.25, 51.722515}, {1.275, 51.403338}, {1.3, 51.107209}, {1.325, 50.832237}, { 1.35, 50.576893}, {1.375, 50.46715}, {1.4, 50.432833}}]}}, {{}, {}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{False, False}, AxesLabel->{None, None}, AxesOrigin->{0.9916666666666691, 0}, DisplayFunction->Identity, Frame->{{True, False}, {True, False}}, FrameLabel->{{None, None}, {None, None}}, FrameStyle->{{ StrokeForm[ Opacity[0]], StrokeForm[ Opacity[0]]}, {Automatic, None}}, FrameTicks->FrontEndValueCache[{{Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}]& , None}, { Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}]& , None}}, {{{{-50., FormBox[ RowBox[{"-", "50"}], TraditionalForm], {0.01, 0.}}, {-25., FormBox[ RowBox[{"-", "25"}], TraditionalForm], {0.01, 0.}}, {0., FormBox["0", TraditionalForm], {0.01, 0.}}, {25., FormBox["25", TraditionalForm], {0.01, 0.}}, {50., FormBox["50", TraditionalForm], {0.01, 0.}}}, None}, {{{1., FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.0\"", ShowStringCharacters -> False], 1.`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.1, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.1\"", ShowStringCharacters -> False], 1.1`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.2, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.2\"", ShowStringCharacters -> False], 1.2`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.3, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.3\"", ShowStringCharacters -> False], 1.3`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.4, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.4\"", ShowStringCharacters -> False], 1.4`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}}, None}}], GridLines->{None, None}, GridLinesStyle->Directive[ GrayLevel[0.4, 0.5], AbsoluteThickness[1], AbsoluteDashing[{1, 2}]], ImageSize->{723.3671875, Automatic}, Method->{ "OptimizePlotMarkers" -> True, "OptimizePlotMarkers" -> True, "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ Identity[ Part[#, 1]], Identity[ Part[#, 2]]}& ), "CopiedValueFunction" -> ({ Identity[ Part[#, 1]], Identity[ Part[#, 2]]}& )}}, PlotRange->{{0.9916666666666691, 1.4}, {-67.071819, 57.406912}}, PlotRangeClipping->True, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.05], Scaled[0.05]}}, Ticks->{Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}, RotateLabel -> 0]& , Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}, RotateLabel -> 0]& }]], "Output",\ CellChangeTimes->{{3.851224944105775*^9, 3.8512250028919086`*^9}, { 3.851225043024221*^9, 3.851225092347924*^9}, 3.851225126310198*^9, 3.851225223079907*^9, {3.851225330489601*^9, 3.851225355948699*^9}, 3.851225389588039*^9}, CellLabel->"Out[25]=",ExpressionUUID->"dad67ae9-473d-49b3-a4ed-6cc27aca3cc2"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"epsZ", "\[LeftDoubleBracket]", RowBox[{"k", ",", "1"}], "\[RightDoubleBracket]"}], ",", RowBox[{"epsZ", "\[LeftDoubleBracket]", RowBox[{"k", ",", "n"}], "\[RightDoubleBracket]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"n", ",", "3", ",", "6"}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", RowBox[{"Length", "[", "eps", "]"}]}], "}"}]}], "]"}], ",", RowBox[{"PlotTheme", "\[Rule]", "\"\\""}], ",", RowBox[{"Joined", "\[Rule]", "True"}]}], "]"}]], "Input", CellChangeTimes->{{3.851225420601947*^9, 3.851225434580069*^9}, { 3.851225492872567*^9, 3.851225492962043*^9}}, CellLabel->"In[34]:=",ExpressionUUID->"e9d7c473-f53c-4be4-9780-1cba856893ff"], Cell[BoxData[ GraphicsBox[{{}, {{}, {}, {RGBColor[0.790588, 0.201176, 0.], PointSize[0.011000000000000001`], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1., 0.001932}, {1.025, 0.001864}, {1.05, 0.0018}, {1.075, 0.001738}, {1.1, 0.00168}, {1.125, 0.001625}, {1.15, 0.001574}, {1.175, 0.001527}, {1.2, 0.001483}, {1.225, 0.001443}, {1.25, 0.001405}, {1.275, 0.001372}, {1.3, 0.001341}, {1.325, 0.001313}, {1.35, 0.001289}, { 1.375, 0.}, {1.4, 0.}}]}, {RGBColor[0.192157, 0.388235, 0.807843], PointSize[0.011000000000000001`], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1., 0.}, {1.025, 0.}, {1.05, 0.}, {1.075, 0.}, {1.1, 0.}, { 1.125, 0.}, {1.15, 0.}, {1.175, 0.}, {1.2, 0.}, {1.225, 0.}, {1.25, 0.}, {1.275, 0.}, {1.3, 0.}, {1.325, 0.}, {1.35, 0.}, {1.375, 0.001369}, {1.4, 0.001375}}]}, {RGBColor[1., 0.607843, 0.], PointSize[0.011000000000000001`], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1., 0.964721}, {1.025, 0.961772}, {1.05, 0.956999}, {1.075, 0.948699}, {1.1, 0.933404}, {1.125, 0.904167}, {1.15, 0.848555}, {1.175, 0.751875}, {1.2, 0.616552}, {1.225, 0.47671}, {1.25, 0.36527}, {1.275, 0.287739}, {1.3, 0.235707}, {1.325, 0.200378}, {1.35, 0.175725}, {1.375, 0.}, {1.4, 0.}}]}, {RGBColor[0., 0.596078, 0.109804], PointSize[0.011000000000000001`], AbsoluteThickness[3], CapForm["Butt"], LineBox[{{1., 0.000059}, {1.025, 0.000852}, {1.05, 0.00331}, {1.075, 0.00914}, {1.1, 0.021813}, {1.125, 0.048282}, {1.15, 0.100987}, {1.175, 0.194635}, {1.2, 0.326815}, {1.225, 0.463419}, {1.25, 0.571546}, {1.275, 0.645708}, {1.3, 0.694337}, {1.325, 0.726254}, {1.35, 0.747506}, { 1.375, 0.91574}, {1.4, 0.915323}}]}}, {{}, {}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{False, False}, AxesLabel->{None, None}, AxesOrigin->{0.9916666666666691, 0}, DisplayFunction->Identity, Frame->{{True, False}, {True, False}}, FrameLabel->{{None, None}, {None, None}}, FrameStyle->{{ StrokeForm[ Opacity[0]], StrokeForm[ Opacity[0]]}, {Automatic, None}}, FrameTicks->FrontEndValueCache[{{Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}]& , None}, { Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}]& , None}}, {{{{0., FormBox["0", TraditionalForm], {0.01, 0.}}, {0.2, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"0.2\"", ShowStringCharacters -> False], 0.2`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 0.4, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"0.4\"", ShowStringCharacters -> False], 0.4`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 0.6, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"0.6\"", ShowStringCharacters -> False], 0.6`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 0.8, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"0.8\"", ShowStringCharacters -> False], 0.8`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, {1., FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.0\"", ShowStringCharacters -> False], 1.`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}}, None}, {{{1., FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.0\"", ShowStringCharacters -> False], 1.`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.1, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.1\"", ShowStringCharacters -> False], 1.1`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.2, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.2\"", ShowStringCharacters -> False], 1.2`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.3, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.3\"", ShowStringCharacters -> False], 1.3`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}, { 1.4, FormBox[ TagBox[ InterpretationBox[ StyleBox["\"1.4\"", ShowStringCharacters -> False], 1.4`15.954589770191003, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 1}]& ], TraditionalForm], {0.01, 0.}}}, None}}], GridLines->{None, None}, GridLinesStyle->Directive[ GrayLevel[0.4, 0.5], AbsoluteThickness[1], AbsoluteDashing[{1, 2}]], Method->{ "OptimizePlotMarkers" -> True, "OptimizePlotMarkers" -> True, "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ Identity[ Part[#, 1]], Identity[ Part[#, 2]]}& ), "CopiedValueFunction" -> ({ Identity[ Part[#, 1]], Identity[ Part[#, 2]]}& )}}, PlotRange->{{0.9916666666666691, 1.4}, {0, 0.964721}}, PlotRangeClipping->True, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.02], Scaled[0.05]}}, Ticks->{Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}, RotateLabel -> 0]& , Charting`FindScaledTicks[ (Charting`SimpleTicks[#, #2, 6]& )[ SlotSequence[1]], {Identity, Identity}, RotateLabel -> 0]& }]], "Output",\ CellChangeTimes->{{3.85122542357023*^9, 3.851225434992806*^9}, { 3.851225486314489*^9, 3.851225493333332*^9}}, CellLabel->"Out[34]=",ExpressionUUID->"2a2efd1e-215b-4367-831c-d3eaaa63ec02"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Downfolding BSE", "Section", CellChangeTimes->{{3.8539418515047903`*^9, 3.853941859257752*^9}},ExpressionUUID->"6a704d60-27a2-4628-a61b-\ b8f4e21f8868"], Cell[BoxData[ RowBox[{ SuperscriptBox["H", RowBox[{"(", "p", ")"}]], "=", RowBox[{"(", "\[NoBreak]", GridBox[{ { SubsuperscriptBox["\[Epsilon]", "p", "HF"], SubsuperscriptBox["V", "p", RowBox[{"2", "h1p"}]], SubsuperscriptBox["V", "p", RowBox[{"2", "p1h"}]]}, { RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "p", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], SuperscriptBox["C", RowBox[{"2", "h1p"}]], "0"}, { RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "p", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], "0", SuperscriptBox["C", RowBox[{"2", "p1h"}]]} }], "\[NoBreak]", ")"}]}]], "Input", CellChangeTimes->{{3.853860765989546*^9, 3.853860843155305*^9}},ExpressionUUID->"6feb960f-bb32-4591-80f4-\ 4f095d8668c2"], Cell[BoxData[ RowBox[{ RowBox[{"Det", "[", RowBox[{ SuperscriptBox["H", RowBox[{"(", "p", ")"}]], "-", RowBox[{"\[Omega]", " ", "1"}]}], "]"}], "==", "0"}]], "Input", CellChangeTimes->{{3.853860845482641*^9, 3.8538608764071417`*^9}},ExpressionUUID->"21c50754-febc-41cd-a91a-\ d483a7bc8140"], Cell[BoxData[ RowBox[{ RowBox[{"Det", "[", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubsuperscriptBox["\[Epsilon]", "p", "HF"], "-", "\[Omega]"}], SubsuperscriptBox["V", "p", RowBox[{"2", "h1p"}]], SubsuperscriptBox["V", "p", RowBox[{"2", "p1h"}]]}, { RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "p", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "1"}]}], "0"}, { RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "p", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], "0", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "1"}]}]} }], "\[NoBreak]", ")"}], "]"}], "==", "0"}]], "Input", CellChangeTimes->{{3.853860882936471*^9, 3.853860914930173*^9}},ExpressionUUID->"4dfd87b2-28e1-4b90-98bd-\ 12ef5c33e7cd"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ SubsuperscriptBox["\[Epsilon]", "p", "HF"], "-", "\[Omega]"}], ")"}], RowBox[{"Det", "[", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "1"}]}], "0"}, {"0", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "1"}]}]} }], "\[NoBreak]", ")"}], "]"}]}], "-", RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "p", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], RowBox[{"(", "\[NoBreak]", GridBox[{ { SubsuperscriptBox["V", "p", RowBox[{"2", "h1p"}]], SubsuperscriptBox["V", "p", RowBox[{"2", "p1h"}]]}, {"0", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "1"}]}]} }], "\[NoBreak]", ")"}]}], "+", RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "p", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], RowBox[{"(", "\[NoBreak]", GridBox[{ { SubsuperscriptBox["V", "p", RowBox[{"2", "h1p"}]], SubsuperscriptBox["V", "p", RowBox[{"2", "p1h"}]]}, { RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "1"}]}], "0"} }], "\[NoBreak]", ")"}]}]}], "=", "0"}]], "Input", CellChangeTimes->{{3.853860944854035*^9, 3.853860994667194*^9}},ExpressionUUID->"f6448161-1952-4500-b5f5-\ 566946f9b807"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ SubsuperscriptBox["\[Epsilon]", "p", "HF"], "-", "\[Omega]"}], ")"}], RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "1"}]}], ")"}], RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "1"}]}], ")"}]}], "-", RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "p", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "1"}]}], ")"}], SubsuperscriptBox["V", "p", RowBox[{"2", "h1p"}]]}], "-", RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "p", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "1"}]}], ")"}], SubsuperscriptBox["V", "p", RowBox[{"2", "p1h"}]]}]}], "=", "0"}]], "Input", CellChangeTimes->{{3.853861004235111*^9, 3.8538610705718946`*^9}},ExpressionUUID->"260633fc-4386-4e7b-a747-\ 77a336ee6b4d"], Cell[BoxData[ RowBox[{ RowBox[{ SubsuperscriptBox["\[Epsilon]", "p", "HF"], "-", "\[Omega]"}], "=", RowBox[{ FractionBox[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "p", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "1"}]}], ")"}], SubsuperscriptBox["V", "p", RowBox[{"2", "h1p"}]]}], "+", RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "p", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "1"}]}], ")"}], SubsuperscriptBox["V", "p", RowBox[{"2", "p1h"}]]}]}], RowBox[{ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "1"}]}], ")"}], RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "1"}]}], ")"}]}]], "=", "0"}]}]], "Input", CellChangeTimes->{{3.853861132474517*^9, 3.8538611458989067`*^9}},ExpressionUUID->"0819721e-8f8a-4961-93d6-\ 77fc2fd42396"] }, Closed]], Cell[CellGroupData[{ Cell["Two-determinant reference", "Section", CellChangeTimes->{{3.853941873054824*^9, 3.853941895786997*^9}, { 3.853994650330038*^9, 3.85399465155588*^9}, {3.854010641568082*^9, 3.854010643582584*^9}},ExpressionUUID->"470a82c0-3bf7-49b2-b0a4-\ e18638c845fc"], Cell[TextData[{ "Let\[CloseCurlyQuote]s consider that additionally to the 1h or 1p reference \ determinant, we now have an additional 2h1p or 2p1h configuration in the \ reference space.\nLet\[CloseCurlyQuote]s denote the reference determinant as \ P (where P can be a particle or a hole) and the 2h1p or 2p1h configuration as \ ", Cell[BoxData[ FormBox["QIA", TraditionalForm]],ExpressionUUID-> "1e30d1d7-03d1-4b6f-8e9a-ca3867a36ad2"], " (where Q can be a particle or a hole)." }], "Text", CellChangeTimes->{{3.8539419915154533`*^9, 3.853942148847609*^9}, { 3.8539946847186537`*^9, 3.853994686507917*^9}, {3.854119054456788*^9, 3.854119123820446*^9}, {3.85411940362047*^9, 3.854119469378769*^9}, { 3.854120228323204*^9, 3.854120229289616*^9}, 3.854120581153137*^9},ExpressionUUID->"0d18b6aa-4968-4bd0-a62c-\ 7cbf1928b263"], Cell[BoxData[ RowBox[{ SuperscriptBox["H", RowBox[{"(", "P", ")"}]], "=", RowBox[{"(", "\[NoBreak]", GridBox[{ { SubsuperscriptBox["\[Epsilon]", "P", "HF"], SubscriptBox["V", RowBox[{"Q", "[", "IA", "]"}]], SubsuperscriptBox["V", "p", RowBox[{"2", "h1p"}]], SubsuperscriptBox["V", "p", RowBox[{"2", "p1h"}]]}, { SubscriptBox["V", RowBox[{"P", ",", RowBox[{"Q", "[", "IA", "]"}]}]], SubscriptBox["C", RowBox[{ RowBox[{"Q", "[", "IA", "]"}], ",", RowBox[{"Q", "[", "IA", "]"}]}]], SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]]}, { RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], SuperscriptBox["C", RowBox[{"2", "h1p"}]], "0"}, { RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], "0", SuperscriptBox["C", RowBox[{"2", "p1h"}]]} }], "\[NoBreak]", ")"}]}]], "Input", CellChangeTimes->{{3.853860765989546*^9, 3.853860843155305*^9}, { 3.853941896875486*^9, 3.853941941030599*^9}, {3.853941981055896*^9, 3.8539419850432796`*^9}, {3.853942156748558*^9, 3.853942157474918*^9}, { 3.853942470091695*^9, 3.853942483640237*^9}, {3.8539426350210333`*^9, 3.853942650511012*^9}, {3.853994680996086*^9, 3.853994703807873*^9}, { 3.853995596018257*^9, 3.8539956365205193`*^9}, {3.853996052084077*^9, 3.853996091861925*^9}, {3.853996294868775*^9, 3.853996330160097*^9}, { 3.853996398976129*^9, 3.853996410667295*^9}, {3.854119126273769*^9, 3.854119129234701*^9}, {3.854119293794915*^9, 3.854119305768619*^9}, { 3.854119477861698*^9, 3.854119478514227*^9}, {3.854120744279851*^9, 3.8541207542482443`*^9}},ExpressionUUID->"de460126-5872-41ad-b94a-\ 2ac25594d244"], Cell["The matrix elements are", "Text",ExpressionUUID->"5ddc87f4-cdbc-4e64-b398-e4dd73a164b9"], Cell[BoxData[ RowBox[{ SubsuperscriptBox["V", RowBox[{"P", ",", RowBox[{"k", "[", "lc", "]"}]}], RowBox[{"2", "h1p"}]], "=", RowBox[{ RowBox[{ SqrtBox["2"], TemplateBox[{"Pc", "kl"}, "BraKet"], "\t", SubsuperscriptBox["V", RowBox[{"P", ",", RowBox[{ RowBox[{"[", "kc", "]"}], "d"}]}], RowBox[{"2", "p1h"}]]}], "=", RowBox[{ SqrtBox["2"], TemplateBox[{"Pk", "dc"}, "BraKet"]}]}]}]], "Input", CellChangeTimes->{{3.8539944371520357`*^9, 3.853994504010198*^9}, { 3.853994657174964*^9, 3.853994662806715*^9}, {3.853994753414856*^9, 3.853994759578096*^9}, 3.853996303420765*^9},ExpressionUUID->"13b10e6f-abda-4091-a5ab-\ 9647b9bd5090"], Cell[BoxData[ RowBox[{ SubscriptBox["V", RowBox[{"P", ",", RowBox[{"Q", "[", "IA", "]"}]}]], "=", RowBox[{ SqrtBox["2"], TemplateBox[{"PA", "QI"}, "BraKet"]}]}]], "Input", CellChangeTimes->{{3.8539947702657337`*^9, 3.8539948131985807`*^9}, { 3.85399629930897*^9, 3.8539963007982683`*^9}, {3.854120213092823*^9, 3.854120216961879*^9}},ExpressionUUID->"8fae97ef-b0a1-4939-9bfa-\ 1b576bff870a"], Cell[BoxData[ RowBox[{ SubsuperscriptBox["C", RowBox[{ RowBox[{"i", "[", "ja", "]"}], ",", RowBox[{"k", "[", "lc", "]"}]}], RowBox[{"2", "h1p"}]], "=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[Epsilon]", "i"], "+", SubscriptBox["\[Epsilon]", "j"], "-", SubscriptBox["\[Epsilon]", "a"]}], ")"}], SubscriptBox["\[Delta]", "jl"], SubscriptBox["\[Delta]", "ac"]}], "-", RowBox[{"2", TemplateBox[{"jc", "al"}, "BraKet"]}]}], ")"}], SubscriptBox["\[Delta]", "ik"], "\t", SubsuperscriptBox["C", RowBox[{ RowBox[{ RowBox[{"[", "ia", "]"}], "b"}], ",", RowBox[{ RowBox[{"[", "kc", "]"}], "d"}]}], RowBox[{"2", "p1h"}]]}], "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[Epsilon]", "a"], "+", SubscriptBox["\[Epsilon]", "b"], "-", SubscriptBox["\[Epsilon]", "i"]}], ")"}], SubscriptBox["\[Delta]", "ik"], SubscriptBox["\[Delta]", "ac"]}], "+", RowBox[{"2", TemplateBox[{"ak", "ic"}, "BraKet"]}]}], ")"}], SubscriptBox["\[Delta]", "bd"]}]}]}]], "Input", CellChangeTimes->{{3.854120312844335*^9, 3.8541203155664053`*^9}, { 3.854120347333592*^9, 3.854120433318367*^9}, {3.854120878817917*^9, 3.8541209016574574`*^9}},ExpressionUUID->"a36084fe-8d84-44a2-ab56-\ 752e26abb5c2"], Cell[BoxData[ RowBox[{ SubscriptBox["C", RowBox[{ RowBox[{"Q", "[", "IA", "]"}], ",", RowBox[{"Q", "[", "IA", "]"}]}]], "=", RowBox[{ RowBox[{"Sign", "[", RowBox[{ SubscriptBox["\[Epsilon]", "Q"], "-", "\[Mu]"}], "]"}], RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["\[Epsilon]", "Q"], "+", SubscriptBox["\[Epsilon]", "A"], "-", SubscriptBox["\[Epsilon]", "I"]}], ")"}], "+", RowBox[{"2", TemplateBox[{"IA", "AI"}, "BraKet"]}]}], ")"}]}]}]], "Input", CellChangeTimes->{{3.853995497349127*^9, 3.853995505457183*^9}, { 3.853995541603786*^9, 3.8539955528216953`*^9}, {3.85399634487328*^9, 3.8539963551113367`*^9}, {3.85412027301052*^9, 3.854120276687199*^9}},ExpressionUUID->"953e39d9-6625-402e-8c90-\ 8a7cb2cccde3"], Cell[BoxData[ RowBox[{ SubsuperscriptBox["C", RowBox[{ RowBox[{"Q", "[", "IA", "]"}], ",", RowBox[{"k", "[", "lc", "]"}]}], RowBox[{"2", "h1p"}]], "=", RowBox[{ RowBox[{ RowBox[{"-", "2"}], TemplateBox[{"Ic", "Al"}, "BraKet"], SubscriptBox["\[Delta]", "Qk"], "\t", SubsuperscriptBox["C", RowBox[{ RowBox[{ RowBox[{"[", "IA", "]"}], "Q"}], ",", RowBox[{ RowBox[{"[", "kc", "]"}], "d"}]}], RowBox[{"2", "p1h"}]]}], "=", RowBox[{ RowBox[{"+", "2"}], TemplateBox[{"Ak", "Ic"}, "BraKet"], SubscriptBox["\[Delta]", "Qd"]}]}]}]], "Input", CellChangeTimes->{{3.854120489513905*^9, 3.8541205118547907`*^9}, { 3.854120541925247*^9, 3.854120559913643*^9}, {3.854120622184505*^9, 3.8541207030246143`*^9}, {3.854120766637642*^9, 3.854120780648139*^9}, { 3.8541208494794207`*^9, 3.8541209095616493`*^9}},ExpressionUUID->"458a09fb-389c-463e-aefa-\ 8294bec583fa"], Cell["Let us now solve the secular equations", "Text",ExpressionUUID->"c90c48af-9fdf-4ddc-8608-9400c30a5610"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubsuperscriptBox["\[Epsilon]", "P", "HF"], "-", "\[Omega]"}], SubscriptBox["V", RowBox[{"Q", "[", "IA", "]"}]], SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]]}, { SubscriptBox["V", RowBox[{"Q", "[", "IA", "]"}]], RowBox[{ SubscriptBox["C", RowBox[{ RowBox[{"Q", "[", "IA", "]"}], ",", RowBox[{"Q", "[", "IA", "]"}]}]], "-", "\[Omega]"}], SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]]}, { RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], "0"}, { RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], "0", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}]} }], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ { SubscriptBox["c", "P"]}, { SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}, { SuperscriptBox["c", RowBox[{"2", "h1p"}]]}, { SuperscriptBox["c", RowBox[{"2", "p1h"}]]} }], "\[NoBreak]", ")"}]}], "==", RowBox[{"(", "\[NoBreak]", GridBox[{ {"0"}, {"0"}, {"0"}, {"0"} }], "\[NoBreak]", ")"}]}]], "Input", CellChangeTimes->{{3.854120937286797*^9, 3.854120976971858*^9}, { 3.85412111123944*^9, 3.854121135956566*^9}, {3.854121314200409*^9, 3.854121318452858*^9}},ExpressionUUID->"3c8afc9a-6104-43d2-8a12-\ a28ea7c2ad67"], Cell["The fourth line yields", "Text",ExpressionUUID->"aafadf45-fa5d-4336-8b76-b63439e28ca0"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", "P"]}], "+", RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}], "+", RowBox[{ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], SuperscriptBox["c", RowBox[{"2", "p1h"}]]}]}], "==", RowBox[{"0", "\t", "\[DoubleLongRightArrow]", "\t", SuperscriptBox["c", RowBox[{"2", "p1h"}]]}], "==", RowBox[{ RowBox[{"-", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]]}], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", "P"]}], "+", RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}]}], ")"}]}]}]], "Input", CellChangeTimes->{{3.854010454233684*^9, 3.854010532192396*^9}, { 3.854010646575485*^9, 3.8540106473948936`*^9}, {3.8541209550372334`*^9, 3.8541209560589457`*^9}, {3.8541209884594193`*^9, 3.8541210005737047`*^9}},ExpressionUUID->"731e5aa2-2627-4749-89ca-\ 13d707fa2305"], Cell["The third line yields", "Text",ExpressionUUID->"4d08ac91-7b28-436a-a672-edd3cf5ebb8f"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", "P"]}], "+", RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}], "+", RowBox[{ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], SuperscriptBox["c", RowBox[{"2", "h1p"}]]}]}], "==", RowBox[{"0", "\t", "\[DoubleLongRightArrow]", "\t", SuperscriptBox["c", RowBox[{"2", "h1p"}]]}], "==", RowBox[{ RowBox[{"-", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]]}], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", "P"]}], "+", RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}]}], ")"}]}]}]], "Input", CellChangeTimes->{{3.854010540138933*^9, 3.854010579623904*^9}, { 3.8540106481750793`*^9, 3.8540106491862783`*^9}, {3.854121003736683*^9, 3.854121017943685*^9}},ExpressionUUID->"09edbc2e-1fd4-47fa-b54f-\ e187cfeccc59"], Cell["The second line yields", "Text",ExpressionUUID->"8e0d45f2-faf4-46af-a8aa-fb7d172b4e8c"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["V", RowBox[{"Q", "[", "IA", "]"}]], SubscriptBox["c", "P"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["C", RowBox[{ RowBox[{"Q", "[", "IA", "]"}], ",", RowBox[{"Q", "[", "IA", "]"}]}]], "-", "\[Omega]"}], ")"}], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}], "+", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], SuperscriptBox["c", RowBox[{"2", "h1p"}]]}], "+", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], SuperscriptBox["c", RowBox[{"2", "p1h"}]]}]}], "==", "0"}], "\t"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[DoubleLongRightArrow]", "\t", SubscriptBox["V", RowBox[{"Q", "[", "IA", "]"}]]}], SubscriptBox["c", "P"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["C", RowBox[{ RowBox[{"Q", "[", "IA", "]"}], ",", RowBox[{"Q", "[", "IA", "]"}]}]], "-", "\[Omega]"}], ")"}], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}], "-", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", "P"]}], "+", RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}]}], ")"}]}], "-", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", "P"]}], "+", RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}]}], ")"}]}]}], "==", "0"}]}], "Input",\ CellChangeTimes->{{3.854010611587925*^9, 3.854010694140316*^9}, { 3.854121023141982*^9, 3.854121057195273*^9}, 3.854121122972999*^9},ExpressionUUID->"f2438676-7819-493d-ac9a-\ 51dc5fb67c04"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[DoubleLongRightArrow]", "\t", SubscriptBox["V", RowBox[{"Q", "[", "IA", "]"}]]}], SubscriptBox["c", "P"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["C", RowBox[{ RowBox[{"Q", "[", "IA", "]"}], ",", RowBox[{"Q", "[", "IA", "]"}]}]], "-", "\[Omega]"}], ")"}], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}], "-", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", "P"]}], "-", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}], "-", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", "P"]}], "-", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}]}], "==", "0"}]], "Input", CellChangeTimes->{{3.854010714623451*^9, 3.854010733338195*^9}, { 3.8541210590283813`*^9, 3.854121082192257*^9}},ExpressionUUID->"02baca0b-7f2f-4be6-826c-\ 0d732408f2ad"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[DoubleLongRightArrow]", "\t", RowBox[{"(", RowBox[{ SubscriptBox["V", RowBox[{"Q", "[", "IA", "]"}]], "-", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}]}], "-", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}]}]}], ")"}]}], SubscriptBox["c", "P"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["C", RowBox[{ RowBox[{"Q", "[", "IA", "]"}], ",", RowBox[{"Q", "[", "IA", "]"}]}]], "-", "\[Omega]"}], ")"}], "-", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}]}], "-", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}]}]}], ")"}], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}]}], "==", "0"}]], "Input", CellChangeTimes->{{3.854010746281262*^9, 3.8540107970959873`*^9}, { 3.8541210848483467`*^9, 3.85412110387169*^9}},ExpressionUUID->"f1fe5e52-9053-451b-8521-\ 6d393ea4a08f"], Cell["The first line yields", "Text",ExpressionUUID->"09951dc5-1207-416a-a2ea-cf6c4c6fc44d"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ SubsuperscriptBox["\[Epsilon]", "P", "HF"], "-", "\[Omega]"}], ")"}], SubscriptBox["c", "P"]}], "+", RowBox[{ SubscriptBox["V", RowBox[{"Q", "[", "IA", "]"}]], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}], "+", RowBox[{ SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], SuperscriptBox["c", RowBox[{"2", "h1p"}]]}], "+", RowBox[{ SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], SuperscriptBox["c", RowBox[{"2", "p1h"}]]}]}], "==", "0"}]], "Input", CellChangeTimes->{ 3.854121107266527*^9, {3.8541211446980553`*^9, 3.8541211510634117`*^9}},ExpressionUUID->"04e3db48-bd52-4a1d-bdea-\ 7c8f4c20e3f6"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[DoubleLongRightArrow]", "\t", RowBox[{"(", RowBox[{ SubsuperscriptBox["\[Epsilon]", "P", "HF"], "-", "\[Omega]"}], ")"}]}], SubscriptBox["c", "P"]}], "+", RowBox[{ SubscriptBox["V", RowBox[{"Q", "[", "IA", "]"}]], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}], "-", RowBox[{ SubsuperscriptBox["V", "p", RowBox[{"2", "h1p"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", "P"]}], "+", RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}]}], ")"}]}], "-", RowBox[{ SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", "P"]}], "+", RowBox[{ RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}]}], ")"}]}]}], "==", "0"}]], "Input", CellChangeTimes->{ 3.854121117923003*^9, {3.854121155430485*^9, 3.8541211670051813`*^9}, { 3.8541213225013227`*^9, 3.854121326236671*^9}},ExpressionUUID->"ab19d3af-3174-4ce8-86b0-\ dcc88d1af0ac"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[DoubleLongRightArrow]", "\t", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ SubsuperscriptBox["\[Epsilon]", "P", "HF"], "-", "\[Omega]"}], ")"}], "-", RowBox[{ SubsuperscriptBox["V", "p", RowBox[{"2", "h1p"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}]}], "-", RowBox[{ SubsuperscriptBox["V", "p", RowBox[{"2", "p1h"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}]}]}], ")"}]}], SubscriptBox["c", "P"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["V", RowBox[{"Q", "[", "IA", "]"}]], "-", RowBox[{ SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}]}], "-", RowBox[{ SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}]}]}], ")"}], SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]}]}], "==", "0"}]], "Input", CellChangeTimes->{{3.8541211690967293`*^9, 3.854121180449953*^9}},ExpressionUUID->"5555ca58-25bc-40bf-9d66-\ 0058a15c72a0"], Cell["Finally, we end up wit the new dynamical system", "Text",ExpressionUUID->"cf5c443b-a1be-47db-8c90-8d92dc005175"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ RowBox[{"(", RowBox[{ SubsuperscriptBox["\[Epsilon]", "P", "HF"], "-", "\[Omega]"}], ")"}], "-", RowBox[{ SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}]}], "-", RowBox[{ SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}]}]}], RowBox[{ SubscriptBox["V", RowBox[{"Q", "[", "IA", "]"}]], "-", RowBox[{ SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}]}], "-", RowBox[{ SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}]}]}]}, { RowBox[{ SubscriptBox["V", RowBox[{"Q", "[", "IA", "]"}]], "-", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}]}], "-", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}]}]}], RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["C", RowBox[{ RowBox[{"Q", "[", "IA", "]"}], ",", RowBox[{"Q", "[", "IA", "]"}]}]], "-", "\[Omega]"}], ")"}], "-", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}]}], "-", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}]}]}]} }], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ { SubscriptBox["c", "P"]}, { SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]} }], "\[NoBreak]", ")"}]}], "==", RowBox[{"(", "\[NoBreak]", GridBox[{ {"0"}, {"0"} }], "\[NoBreak]", ")"}]}]], "Input", CellChangeTimes->{{3.8541211857211227`*^9, 3.854121230232273*^9}},ExpressionUUID->"009c187a-6ffb-4145-8afd-\ 433506865326"], Cell["with elements", "Text",ExpressionUUID->"0581ffe5-a1bd-456d-b8ca-274d0988b17f"], Cell[BoxData[ FrameBox[ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[CapitalSigma]", "P"], "[", "\[Omega]", "]"}], "=", RowBox[{ RowBox[{ RowBox[{"-", SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]]}], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}]}], "-", RowBox[{ SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}]}]}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["\[CapitalSigma]", RowBox[{"Q", "[", "IA", "]"}]], "[", "\[Omega]", "]"}], "=", RowBox[{ RowBox[{ RowBox[{"-", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]]}], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}]}], "-", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}]}]}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["\[CapitalSigma]", RowBox[{ RowBox[{"Q", "[", "IA", "]"}], ",", "P"}]], "[", "\[Omega]", "]"}], "=", RowBox[{ RowBox[{ RowBox[{"-", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]]}], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}]}], "-", RowBox[{ SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}]}]}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["\[CapitalSigma]", RowBox[{"P", ",", RowBox[{"Q", "[", "IA", "]"}]}]], "[", "\[Omega]", "]"}], "=", RowBox[{ RowBox[{ RowBox[{"-", SubsuperscriptBox["V", "P", RowBox[{"2", "h1p"}]]}], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "h1p"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "h1p"}]], ")"}], "\[Transpose]"}]}], "-", RowBox[{ SubsuperscriptBox["V", "P", RowBox[{"2", "p1h"}]], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["C", RowBox[{"2", "p1h"}]], "-", RowBox[{"\[Omega]", " ", "I"}]}], ")"}], RowBox[{"-", "1"}]], RowBox[{ RowBox[{"(", SubsuperscriptBox["C", RowBox[{"Q", "[", "IA", "]"}], RowBox[{"2", "p1h"}]], ")"}], "\[Transpose]"}]}]}]}]}]]], "Input", CellChangeTimes->{{3.854121250195992*^9, 3.854121280870821*^9}},ExpressionUUID->"7bc8daef-44bc-447f-8659-\ e2e31520db06"], Cell["The final result is", "Text",ExpressionUUID->"53ef96ad-c734-44f1-8123-1d211616b540"], Cell[BoxData[ RowBox[{"\[Therefore]", RowBox[{ RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ SubsuperscriptBox["\[Epsilon]", "P", "HF"], "+", RowBox[{ SubscriptBox["\[CapitalSigma]", "P"], "[", "\[Omega]", "]"}], "-", "\[Omega]"}], RowBox[{ SubscriptBox["V", RowBox[{"Q", "[", "IA", "]"}]], "+", RowBox[{ SubscriptBox["\[CapitalSigma]", RowBox[{"P", ",", RowBox[{"Q", "[", "IA", "]"}]}]], "[", "\[Omega]", "]"}]}]}, { RowBox[{ SubscriptBox["V", RowBox[{"Q", "[", "IA", "]"}]], "+", RowBox[{ SubscriptBox["\[CapitalSigma]", RowBox[{ RowBox[{"Q", "[", "IA", "]"}], ",", "P"}]], "[", "\[Omega]", "]"}]}], RowBox[{ SubscriptBox["C", RowBox[{ RowBox[{"Q", "[", "IA", "]"}], ",", RowBox[{"Q", "[", "IA", "]"}]}]], "+", RowBox[{ SubscriptBox["\[CapitalSigma]", RowBox[{"Q", "[", "IA", "]"}]], "[", "\[Omega]", "]"}], "-", "\[Omega]"}]} }], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ { SubscriptBox["c", "P"]}, { SubscriptBox["c", RowBox[{"Q", "[", "IA", "]"}]]} }], "\[NoBreak]", ")"}]}], "==", RowBox[{"(", "\[NoBreak]", GridBox[{ {"0"}, {"0"} }], "\[NoBreak]", ")"}]}]}]], "Input", CellChangeTimes->{{3.854121286300622*^9, 3.854121308654326*^9}},ExpressionUUID->"920b9a14-7358-437b-8b2d-\ 9af272494adb"] }, Open ]] }, WindowSize->{1998, 1395}, WindowMargins->{{2, Automatic}, {Automatic, 0}}, PrintingCopies->1, PrintingPageRange->{1, Automatic}, Magnification:>1.25 Inherited, FrontEndVersion->"13.0 for Mac OS X x86 (64-bit) (December 2, 2021)", StyleDefinitions->"Default.nb", ExpressionUUID->"c947be63-9aef-4192-bf26-b635965432d0" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[580, 22, 88, 0, 84, "Section",ExpressionUUID->"a68e1e90-2158-4da8-9829-76467decd8c9"], Cell[671, 24, 1276, 35, 90, "Input",ExpressionUUID->"682f75fb-1edd-4aa6-a4ad-b597c5f869c9"], Cell[1950, 61, 1001, 27, 64, "Input",ExpressionUUID->"35c12977-2872-4eab-be4f-329f455172b3"], Cell[CellGroupData[{ Cell[2976, 92, 328, 7, 37, "Input",ExpressionUUID->"59810817-5144-4818-800a-a2ceb8fcd500"], Cell[3307, 101, 4095, 96, 308, "Output",ExpressionUUID->"814e3769-9eaf-4e1a-8956-617c8e61d77e"] }, Open ]], Cell[7417, 200, 1274, 35, 90, "Input",ExpressionUUID->"5f735bd6-ba1a-4987-b9f7-8ff4ac674345"], Cell[8694, 237, 981, 27, 64, "Input",ExpressionUUID->"5928cf25-152d-4cb2-9ce3-3f99ce9557d3"], Cell[CellGroupData[{ Cell[9700, 268, 310, 7, 37, "Input",ExpressionUUID->"33a86cd9-4a3d-4b09-91de-2cbb886a6250"], Cell[10013, 277, 5200, 125, 308, "Output",ExpressionUUID->"d32fbdb3-4ad8-4d05-aa55-4c32ff841fbc"] }, Open ]], Cell[15228, 405, 1275, 35, 90, "Input",ExpressionUUID->"051138e6-33b2-49e1-b570-b5e33fd33d7f"], Cell[16506, 442, 982, 27, 64, "Input",ExpressionUUID->"37bd2bc4-e119-4f55-88d4-845984e63c22"], Cell[17491, 471, 230, 6, 37, "Input",ExpressionUUID->"c2496421-c71c-4de1-a28d-dd9067951fda"], Cell[CellGroupData[{ Cell[17746, 481, 312, 7, 37, "Input",ExpressionUUID->"bbbc4763-dda3-4da9-8ff0-9b7dc9932b23"], Cell[18061, 490, 4933, 120, 306, "Output",ExpressionUUID->"cad1c286-e9fa-457d-9d0f-e5060da9432b"] }, Open ]], Cell[23009, 613, 513, 11, 64, "Input",ExpressionUUID->"c351c0eb-ffe9-41ea-b9a4-ee9c001a879d"], Cell[CellGroupData[{ Cell[23547, 628, 1050, 23, 37, "Input",ExpressionUUID->"3dc691e1-f05a-4c4c-8978-c337f01f76cf"], Cell[24600, 653, 8346, 163, 583, "Output",ExpressionUUID->"dad67ae9-473d-49b3-a4ed-6cc27aca3cc2"] }, Open ]], Cell[CellGroupData[{ Cell[32983, 821, 859, 20, 37, "Input",ExpressionUUID->"e9d7c473-f53c-4be4-9780-1cba856893ff"], Cell[33845, 843, 6570, 149, 308, "Output",ExpressionUUID->"2a2efd1e-215b-4367-831c-d3eaaa63ec02"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[40464, 998, 162, 3, 65, "Section",ExpressionUUID->"6a704d60-27a2-4628-a61b-b8f4e21f8868"], Cell[40629, 1003, 878, 28, 116, "Input",ExpressionUUID->"6feb960f-bb32-4591-80f4-4f095d8668c2"], Cell[41510, 1033, 316, 9, 40, "Input",ExpressionUUID->"21c50754-febc-41cd-a91a-d483a7bc8140"], Cell[41829, 1044, 1051, 32, 116, "Input",ExpressionUUID->"4dfd87b2-28e1-4b90-98bd-12ef5c33e7cd"], Cell[42883, 1078, 1724, 56, 68, "Input",ExpressionUUID->"f6448161-1952-4500-b5f5-566946f9b807"], Cell[44610, 1136, 1288, 43, 42, "Input",ExpressionUUID->"260633fc-4386-4e7b-a747-77a336ee6b4d"], Cell[45901, 1181, 1348, 44, 79, "Input",ExpressionUUID->"0819721e-8f8a-4961-93d6-77fc2fd42396"] }, Closed]], Cell[CellGroupData[{ Cell[47286, 1230, 264, 4, 65, "Section",ExpressionUUID->"470a82c0-3bf7-49b2-b0a4-e18638c845fc"], Cell[47553, 1236, 845, 16, 73, "Text",ExpressionUUID->"0d18b6aa-4968-4bd0-a62c-7cbf1928b263"], Cell[48401, 1254, 2386, 63, 146, "Input",ExpressionUUID->"de460126-5872-41ad-b94a-2ac25594d244"], Cell[50790, 1319, 94, 0, 44, "Text",ExpressionUUID->"5ddc87f4-cdbc-4e64-b398-e4dd73a164b9"], Cell[50887, 1321, 726, 24, 43, "Input",ExpressionUUID->"13b10e6f-abda-4091-a5ab-9647b9bd5090"], Cell[51616, 1347, 423, 12, 42, "Input",ExpressionUUID->"8fae97ef-b0a1-4939-9bfa-1b576bff870a"], Cell[52042, 1361, 1532, 48, 44, "Input",ExpressionUUID->"a36084fe-8d84-44a2-ab56-752e26abb5c2"], Cell[53577, 1411, 829, 24, 40, "Input",ExpressionUUID->"953e39d9-6625-402e-8c90-8a7cb2cccde3"], Cell[54409, 1437, 970, 30, 43, "Input",ExpressionUUID->"458a09fb-389c-463e-aefa-8294bec583fa"], Cell[55382, 1469, 109, 0, 44, "Text",ExpressionUUID->"c90c48af-9fdf-4ddc-8608-9400c30a5610"], Cell[55494, 1471, 2424, 78, 146, "Input",ExpressionUUID->"3c8afc9a-6104-43d2-8a12-a28ea7c2ad67"], Cell[57921, 1551, 93, 0, 44, "Text",ExpressionUUID->"aafadf45-fa5d-4336-8b76-b63439e28ca0"], Cell[58017, 1553, 1764, 57, 47, "Input",ExpressionUUID->"731e5aa2-2627-4749-89ca-13d707fa2305"], Cell[59784, 1612, 92, 0, 44, "Text",ExpressionUUID->"4d08ac91-7b28-436a-a672-edd3cf5ebb8f"], Cell[59879, 1614, 1709, 56, 47, "Input",ExpressionUUID->"09edbc2e-1fd4-47fa-b54f-e187cfeccc59"], Cell[61591, 1672, 93, 0, 44, "Text",ExpressionUUID->"8e0d45f2-faf4-46af-a8aa-fb7d172b4e8c"], Cell[61687, 1674, 3079, 103, 79, "Input",ExpressionUUID->"f2438676-7819-493d-ac9a-51dc5fb67c04"], Cell[64769, 1779, 2628, 88, 47, "Input",ExpressionUUID->"02baca0b-7f2f-4be6-826c-0d732408f2ad"], Cell[67400, 1869, 2765, 86, 47, "Input",ExpressionUUID->"f1fe5e52-9053-451b-8521-6d393ea4a08f"], Cell[70168, 1957, 92, 0, 44, "Text",ExpressionUUID->"09951dc5-1207-416a-a2ea-cf6c4c6fc44d"], Cell[70263, 1959, 777, 26, 43, "Input",ExpressionUUID->"04e3db48-bd52-4a1d-bdea-7c8f4c20e3f6"], Cell[71043, 1987, 2132, 70, 47, "Input",ExpressionUUID->"ab19d3af-3174-4ce8-86b0-dcc88d1af0ac"], Cell[73178, 2059, 2498, 79, 47, "Input",ExpressionUUID->"5555ca58-25bc-40bf-9d66-0058a15c72a0"], Cell[75679, 2140, 118, 0, 44, "Text",ExpressionUUID->"cf5c443b-a1be-47db-8c90-8d92dc005175"], Cell[75800, 2142, 5152, 158, 84, "Input",ExpressionUUID->"009c187a-6ffb-4145-8afd-433506865326"], Cell[80955, 2302, 84, 0, 44, "Text",ExpressionUUID->"0581ffe5-a1bd-456d-b8ca-274d0988b17f"], Cell[81042, 2304, 4648, 154, 167, "Input",ExpressionUUID->"7bc8daef-44bc-447f-8659-e2e31520db06"], Cell[85693, 2460, 90, 0, 44, "Text",ExpressionUUID->"53ef96ad-c734-44f1-8123-1d211616b540"], Cell[85786, 2462, 1629, 50, 64, "Input",ExpressionUUID->"920b9a14-7358-437b-8b2d-9af272494adb"] }, Open ]] } ] *)