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@ -105,7 +105,7 @@
$$ E \approx \frac{1}{M} \sum_{i=1}^M E_L(\mathbf{r}_i} \,. $$ E \approx \frac{1}{M} \sum_{i=1}^M E_L(\mathbf{r}_i} \,.
* Numerical evaluation of the energy of the hydrogen atoms * Numerical evaluation of the energy of the hydrogen atom
In this section, we consider the hydrogen atom with the following In this section, we consider the hydrogen atom with the following
wave function: wave function:
@ -121,10 +121,7 @@
\hat{H} = \hat{T} + \hat{V} = - \frac{1}{2} \Delta - \frac{1}{|\mathbf{r}|} \hat{H} = \hat{T} + \hat{V} = - \frac{1}{2} \Delta - \frac{1}{|\mathbf{r}|}
$$ $$
To do that, we will compute the local energy, defined as To do that, we will compute the local energy and check whether it is constant.
and check whether it is constant.
** Local energy ** Local energy
:PROPERTIES: :PROPERTIES:
@ -132,6 +129,8 @@
:header-args:f90: :tangle hydrogen.f90 :header-args:f90: :tangle hydrogen.f90
:END: :END:
You will now program all quantities needed to compute the local energy of the H atom for the given wave function.
Write all the functions of this section in a single file : Write all the functions of this section in a single file :
~hydrogen.py~ if you use Python, or ~hydrogen.f90~ is you use ~hydrogen.py~ if you use Python, or ~hydrogen.f90~ is you use
Fortran. Fortran.