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@ -60,7 +60,7 @@
All the quantities are expressed in /atomic units/ (energies,
coordinates, etc).
** Energy and local energy
** Energy and local energy
For a given system with Hamiltonian $\hat{H}$ and wave function $\Psi$, we define the local energy as
@ -105,7 +105,7 @@
$$ E \approx \frac{1}{M} \sum_{i=1}^M E_L(\mathbf{r}_i} \,.
* Numerical evaluation of the energy of the hydrogen atoms
* Numerical evaluation of the energy of the hydrogen atom
In this section, we consider the hydrogen atom with the following
wave function:
@ -121,10 +121,7 @@
\hat{H} = \hat{T} + \hat{V} = - \frac{1}{2} \Delta - \frac{1}{|\mathbf{r}|}
$$
To do that, we will compute the local energy, defined as
and check whether it is constant.
To do that, we will compute the local energy and check whether it is constant.
** Local energy
:PROPERTIES:
@ -132,6 +129,8 @@
:header-args:f90: :tangle hydrogen.f90
: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 :
~hydrogen.py~ if you use Python, or ~hydrogen.f90~ is you use
Fortran.