From 1c5e6a9cb448d2dfbdf27f1584ac3d925629f944 Mon Sep 17 00:00:00 2001 From: filippi-claudia <44236509+filippi-claudia@users.noreply.github.com> Date: Sat, 30 Jan 2021 22:59:13 +0100 Subject: [PATCH] some more changes --- QMC.org | 15 +++++++-------- 1 file changed, 7 insertions(+), 8 deletions(-) diff --git a/QMC.org b/QMC.org index d544561..9ee8f80 100644 --- a/QMC.org +++ b/QMC.org @@ -59,8 +59,8 @@ 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. @@ -207,7 +206,7 @@ double precision function potential(r) end function potential #+END_SRC -*** Exercise 2 +*** Exercise 2 #+begin_exercise Write a function which computes the wave function at $\mathbf{r}$. The function accepts a scalar =a= and a 3-dimensional vector =r= as