diff --git a/Notebooks/images/0_1_11.tikz b/Notebooks/images/0_1_11.tikz new file mode 100644 index 0000000..61ded10 --- /dev/null +++ b/Notebooks/images/0_1_11.tikz @@ -0,0 +1,37 @@ +\begin{tikzpicture} +\input{Electrons.tikz} + +% Det |I> +\renewcommand{\XX}{\XI} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\updna{\XX}{0.5} +\updn{\XX}{0.} + +% Det |alpha> +\renewcommand{\XX}{\XA} +\cabs{ +\emp{\XX}{2.5} +\upa{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\dn{\XX}{0.5} +\updn{\XX}{0.} + +% Det |J> +\renewcommand{\XX}{\XJ} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\updna{\XX}{0.5} +\updn{\XX}{0.} + +\end{tikzpicture} diff --git a/Notebooks/images/0_1_22.tikz b/Notebooks/images/0_1_22.tikz new file mode 100644 index 0000000..cad0952 --- /dev/null +++ b/Notebooks/images/0_1_22.tikz @@ -0,0 +1,37 @@ +\begin{tikzpicture} +\input{Electrons.tikz} + +% Det |I> +\renewcommand{\XX}{\XI} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\updnab{\XX}{0.5} +\updn{\XX}{0.} + +% Det |alpha> +\renewcommand{\XX}{\XA} +\cabs{ +\emp{\XX}{2.5} +\upa{\XX}{2.0} +} +\emp{\XX}{1.5} +\dnb{\XX}{1.0} +\emp{\XX}{0.5} +\updn{\XX}{0.} + +% Det |J> +\renewcommand{\XX}{\XJ} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\updnab{\XX}{0.5} +\updn{\XX}{0.} + +\end{tikzpicture} diff --git a/Notebooks/images/0_2_22.tikz b/Notebooks/images/0_2_22.tikz new file mode 100644 index 0000000..5987dcc --- /dev/null +++ b/Notebooks/images/0_2_22.tikz @@ -0,0 +1,37 @@ +\begin{tikzpicture} +\input{Electrons.tikz} + +% Det |I> +\renewcommand{\XX}{\XI} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\updnab{\XX}{0.5} +\updn{\XX}{0.} + +% Det |alpha> +\renewcommand{\XX}{\XA} +\cabs{ +\emp{\XX}{2.5} +\updnab{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\emp{\XX}{0.5} +\updn{\XX}{0.} + +% Det |J> +\renewcommand{\XX}{\XJ} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\updnab{\XX}{0.5} +\updn{\XX}{0.} + +\end{tikzpicture} diff --git a/Notebooks/images/1_1_11.tikz b/Notebooks/images/1_1_11.tikz new file mode 100644 index 0000000..d629dce --- /dev/null +++ b/Notebooks/images/1_1_11.tikz @@ -0,0 +1,37 @@ +\begin{tikzpicture} +\input{Electrons.tikz} + +% Det |I> +\renewcommand{\XX}{\XI} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\updna{\XX}{0.5} +\updn{\XX}{0.} + +% Det |alpha> +\renewcommand{\XX}{\XA} +\cabs{ +\emp{\XX}{2.5} +\upa{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\dn{\XX}{0.5} +\updn{\XX}{0.} + +% Det |J> +\renewcommand{\XX}{\XJ} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\upa{\XX}{1.0} +\dn{\XX}{0.5} +\updn{\XX}{0.} + +\end{tikzpicture} diff --git a/Notebooks/images/1_1_12.tikz b/Notebooks/images/1_1_12.tikz new file mode 100644 index 0000000..828d7bd --- /dev/null +++ b/Notebooks/images/1_1_12.tikz @@ -0,0 +1,37 @@ +\begin{tikzpicture} +\input{Electrons.tikz} + +% Det |I> +\renewcommand{\XX}{\XI} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\updnab{\XX}{0.5} +\updn{\XX}{0.} + +% Det |alpha> +\renewcommand{\XX}{\XA} +\cabs{ +\emp{\XX}{2.5} +\upa{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\dnb{\XX}{0.5} +\updn{\XX}{0.} + +% Det |J> +\renewcommand{\XX}{\XJ} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\dnb{\XX}{1.0} +\upa{\XX}{0.5} +\updn{\XX}{0.} + +\end{tikzpicture} diff --git a/Notebooks/images/1_1_21.tikz b/Notebooks/images/1_1_21.tikz new file mode 100644 index 0000000..4975d88 --- /dev/null +++ b/Notebooks/images/1_1_21.tikz @@ -0,0 +1,37 @@ +\begin{tikzpicture} +\input{Electrons.tikz} + +% Det |I> +\renewcommand{\XX}{\XI} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\updnab{\XX}{0.5} +\updn{\XX}{0.} + +% Det |alpha> +\renewcommand{\XX}{\XA} +\cabs{ +\emp{\XX}{2.5} +\upa{\XX}{2.0} +} +\emp{\XX}{1.5} +\dnb{\XX}{1.0} +\emp{\XX}{0.5} +\updn{\XX}{0.} + +% Det |J> +\renewcommand{\XX}{\XJ} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\dnb{\XX}{1.0} +\upa{\XX}{0.5} +\updn{\XX}{0.} + +\end{tikzpicture} diff --git a/Notebooks/images/1_1_22.tikz b/Notebooks/images/1_1_22.tikz new file mode 100644 index 0000000..e0beb3d --- /dev/null +++ b/Notebooks/images/1_1_22.tikz @@ -0,0 +1,37 @@ +\begin{tikzpicture} +\input{Electrons.tikz} + +% Det |I> +\renewcommand{\XX}{\XI} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\updnab{\XX}{0.5} +\updn{\XX}{0.} + +% Det |alpha> +\renewcommand{\XX}{\XA} +\cabs{ +\emp{\XX}{2.5} +\upa{\XX}{2.0} +} +\emp{\XX}{1.5} +\dnb{\XX}{1.0} +\emp{\XX}{0.5} +\updn{\XX}{0.} + +% Det |J> +\renewcommand{\XX}{\XJ} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\dnb{\XX}{1.5} +\emp{\XX}{1.0} +\upa{\XX}{0.5} +\updn{\XX}{0.} + +\end{tikzpicture} diff --git a/Notebooks/images/1_2_22.tikz b/Notebooks/images/1_2_22.tikz new file mode 100644 index 0000000..196f5b5 --- /dev/null +++ b/Notebooks/images/1_2_22.tikz @@ -0,0 +1,37 @@ +\begin{tikzpicture} +\input{Electrons.tikz} + +% Det |I> +\renewcommand{\XX}{\XI} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\updnab{\XX}{0.5} +\updn{\XX}{0.} + +% Det |alpha> +\renewcommand{\XX}{\XA} +\cabs{ +\emp{\XX}{2.5} +\updnab{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\emp{\XX}{0.5} +\updn{\XX}{0.} + +% Det |J> +\renewcommand{\XX}{\XJ} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\dnb{\XX}{1.0} +\upa{\XX}{0.5} +\updn{\XX}{0.} + +\end{tikzpicture} diff --git a/Notebooks/images/2_1_12.tikz b/Notebooks/images/2_1_12.tikz new file mode 100644 index 0000000..509b5d3 --- /dev/null +++ b/Notebooks/images/2_1_12.tikz @@ -0,0 +1,37 @@ +\begin{tikzpicture} +\input{Electrons.tikz} + +% Det |I> +\renewcommand{\XX}{\XI} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\updnab{\XX}{0.5} +\updn{\XX}{0.} + +% Det |alpha> +\renewcommand{\XX}{\XA} +\cabs{ +\emp{\XX}{2.5} +\upa{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\dnb{\XX}{0.5} +\updn{\XX}{0.} + +% Det |J> +\renewcommand{\XX}{\XJ} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\updnab{\XX}{1.0} +\emp{\XX}{0.5} +\updn{\XX}{0.} + +\end{tikzpicture} diff --git a/Notebooks/images/2_1_21.tikz b/Notebooks/images/2_1_21.tikz new file mode 100644 index 0000000..6dfb7ae --- /dev/null +++ b/Notebooks/images/2_1_21.tikz @@ -0,0 +1,37 @@ +\begin{tikzpicture} +\input{Electrons.tikz} + +% Det |I> +\renewcommand{\XX}{\XI} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\updnab{\XX}{0.5} +\updn{\XX}{0.} + +% Det |alpha> +\renewcommand{\XX}{\XA} +\cabs{ +\emp{\XX}{2.5} +\upa{\XX}{2.0} +} +\emp{\XX}{1.5} +\dnb{\XX}{1.0} +\emp{\XX}{0.5} +\updn{\XX}{0.} + +% Det |J> +\renewcommand{\XX}{\XJ} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\updnab{\XX}{1.0} +\emp{\XX}{0.5} +\updn{\XX}{0.} + +\end{tikzpicture} diff --git a/Notebooks/images/2_1_22.tikz b/Notebooks/images/2_1_22.tikz new file mode 100644 index 0000000..87936de --- /dev/null +++ b/Notebooks/images/2_1_22.tikz @@ -0,0 +1,37 @@ +\begin{tikzpicture} +\input{Electrons.tikz} + +% Det |I> +\renewcommand{\XX}{\XI} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\updnab{\XX}{0.5} +\updn{\XX}{0.} + +% Det |alpha> +\renewcommand{\XX}{\XA} +\cabs{ +\emp{\XX}{2.5} +\upa{\XX}{2.0} +} +\emp{\XX}{1.5} +\dnb{\XX}{1.0} +\emp{\XX}{0.5} +\updn{\XX}{0.} + +% Det |J> +\renewcommand{\XX}{\XJ} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\dnb{\XX}{1.5} +\upa{\XX}{1.0} +\emp{\XX}{0.5} +\updn{\XX}{0.} + +\end{tikzpicture} diff --git a/Notebooks/images/2_2_22.tikz b/Notebooks/images/2_2_22.tikz new file mode 100644 index 0000000..72eb4c4 --- /dev/null +++ b/Notebooks/images/2_2_22.tikz @@ -0,0 +1,37 @@ +\begin{tikzpicture} +\input{Electrons.tikz} + +% Det |I> +\renewcommand{\XX}{\XI} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\updnab{\XX}{0.5} +\updn{\XX}{0.} + +% Det |alpha> +\renewcommand{\XX}{\XA} +\cabs{ +\emp{\XX}{2.5} +\updnab{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\emp{\XX}{0.5} +\updn{\XX}{0.} + +% Det |J> +\renewcommand{\XX}{\XJ} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\updnab{\XX}{1.0} +\emp{\XX}{0.5} +\updn{\XX}{0.} + +\end{tikzpicture} diff --git a/Notebooks/images/3_1_22.tikz b/Notebooks/images/3_1_22.tikz new file mode 100644 index 0000000..fd86140 --- /dev/null +++ b/Notebooks/images/3_1_22.tikz @@ -0,0 +1,37 @@ +\begin{tikzpicture} +\input{Electrons.tikz} + +% Det |I> +\renewcommand{\XX}{\XI} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\emp{\XX}{1.5} +\emp{\XX}{1.0} +\updnab{\XX}{0.5} +\updnc{\XX}{0.} + +% Det |alpha> +\renewcommand{\XX}{\XA} +\cabs{ +\emp{\XX}{2.5} +\upa{\XX}{2.0} +} +\emp{\XX}{1.5} +\dnb{\XX}{1.0} +\emp{\XX}{0.5} +\updnc{\XX}{0.} + +% Det |J> +\renewcommand{\XX}{\XJ} +\cabs{ +\emp{\XX}{2.5} +\emp{\XX}{2.0} +} +\upa{\XX}{1.5} +\updncb{\XX}{1.0} +\emp{\XX}{0.5} +\dn{\XX}{0.} + +\end{tikzpicture} diff --git a/Notebooks/images/Electrons.tikz b/Notebooks/images/Electrons.tikz new file mode 100644 index 0000000..dccbecd --- /dev/null +++ b/Notebooks/images/Electrons.tikz @@ -0,0 +1,135 @@ +% Documentation +% ------------- +% +% \up : up electron (black) +% \upr : up electron (red) +% \dn : down electron (black) +% \dnr : down electron (red) +% \updn : up electron (black), down electron (black) +% \updnrr : up electron (red ), down electron (red ) +% \updnrb : up electron (red ), down electron (black) +% \updnbr : up electron (black), down electron (red ) +% \emp : empty orbital +% \cabs{ } : CABS space inside +% +% Example +% ------- +% +% \input{Electrons.tikz} +% +% \cabs{ +% \emp{0.}{2.0} +% \emp{0.}{1.5} +% } +% \emp{0.}{1.0} +% \updnrb{0.}{0.5} +% \updn{0.}{0.} +% + +% Electron symbol +\newcommand{\upel}{$\uparrow$} +\newcommand{\dnel}{$\downarrow$} + +% Colors +\newcommand{\cabs}[1]{ { \color{lightgray}{#1} } } +\newcommand{\obs}[1]{ { \color{black}{#1} } } +\newcommand{\exca}[1]{ { \color{red}{#1} } } +\newcommand{\excb}[1]{ { \color{Cyan}{#1} } } +\newcommand{\excc}[1]{ { \color{Green}{#1} } } +\newcommand{\noexc}[1]{{ \color{black}{#1} } } + +% Spacing between the 3 diagrams +\newcommand{\XI}{-1.} +\newcommand{\XA}{0.} +\newcommand{\XJ}{1.} + +% Up electron +\newcommand{\up}[2]{ + \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); + \node at (#1-0.1,#2) {\noexc{\upel}}; +} + +\newcommand{\upa}[2]{ + \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); + \node at (#1-0.1,#2) {\exca{\upel}}; +} + +\newcommand{\upb}[2]{ + \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); + \node at (#1-0.1,#2) {\excb{\upel}}; +} + +\newcommand{\upc}[2]{ + \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); + \node at (#1-0.1,#2) {\excc{\upel}}; +} + +% Down electron +\newcommand{\dn}[2]{ + \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); + \node at (#1+0.1,#2) {\noexc{\dnel}}; +} + +\newcommand{\dna}[2]{ + \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); + \node at (#1+0.1,#2) {\exca{\dnel}}; +} + +\newcommand{\dnb}[2]{ + \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); + \node at (#1+0.1,#2) {\excb{\dnel}}; +} + +\newcommand{\dnc}[2]{ + \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); + \node at (#1+0.1,#2) {\excc{\dnel}}; +} + +% Up and Down electrons +\newcommand{\updn}[2]{ + \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); + \node at (#1+0.1,#2) {\noexc{\dnel}}; + \node at (#1-0.1,#2) {\noexc{\upel}}; +} + +\newcommand{\updnab}[2]{ + \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); + \node at (#1+0.1,#2) {\excb{\dnel}}; + \node at (#1-0.1,#2) {\exca{\upel}}; +} + +\newcommand{\updncb}[2]{ + \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); + \node at (#1+0.1,#2) {\excb{\dnel}}; + \node at (#1-0.1,#2) {\excc{\upel}}; +} + +\newcommand{\updna}[2]{ + \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); + \node at (#1+0.1,#2) {\noexc{\dnel}}; + \node at (#1-0.1,#2) {\exca{\upel}}; +} + +\newcommand{\updnb}[2]{ + \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); + \node at (#1-0.1,#2) {\noexc{\upel}}; + \node at (#1+0.1,#2) {\excb{\dnel}}; +} + +\newcommand{\updnc}[2]{ + \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); + \node at (#1+0.1,#2) {\noexc{\dnel}}; + \node at (#1-0.1,#2) {\excc{\upel}}; +} + +% Empty orbital +\newcommand{\emp}[2]{ + \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); +} + +% Determinant label +\node at (\XI,-0.7) {$\ket{I}$}; +\node at (\XA,-0.7) {$\ket{\alpha}$}; +\node at (\XJ,-0.7) {$\ket{J}$}; + +\newcommand{\XX}{0.}