Added illustrations

TREX-CoE · Jan 24, 2023 · 2ffd2af · 2ffd2af
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diff --git a/H2_traj.png b/H2_traj.png
diff --git a/H2_traj2.png b/H2_traj2.png
diff --git a/QMC.org b/QMC.org
@@ -1014,7 +1014,6 @@ plot './data' index 0 using 1:2 with lines title 'a=0.1', \
    - The energy is evaluated only inside the box (incompleteness of the space)
    #+end_note
 
-
 *** Exercise
      #+begin_exercise
     Compute a numerical estimate of the energy using a grid of
@@ -2731,10 +2730,14 @@ gcc hydrogen.c qmc_stats.c qmc_metropolis.c -lm -o qmc_metropolis
 
    where $\chi$ is a Gaussian random variable with zero mean and
    variance $\delta t$.
+
+   Here is an illustration of a trajectory:
+   [[./H2_traj.png]]
+
+   Averaging all the trajectories converges to the density of the
+   hydrogen atom.
+   [[./H2_traj2.png]]
 
-   # TODO
-   #    prod    = np.dot((d_new + d_old), (r_new - r_old))
-   #    argexpo = 0.5 * (d2_new - d2_old)*dt + prod
    The algorithm of the previous exercise is only slightly modified as:
 
    1) Evaluate the local energy at $\mathbf{r}_{n}$ and accumulate it

diff --git a/qmc_uniform.py b/qmc_uniform.py
@@ -19,7 +19,7 @@ def MonteCarlo(a, nmax):
      return energy / normalization
 
 a    = 1.2
-nmax = 10000
+nmax = 100000
 
 X = [MonteCarlo(a,nmax) for i in range(30)]
 E, deltaE = ave_error(X)