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Solutions in C up to 3.4
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7
.gitignore
vendored
7
.gitignore
vendored
@ -1,2 +1,7 @@
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__pycache__
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plt_dat
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data
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data
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get_energ
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get_var
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qmc_uni
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qmc_met
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35
energy_hydrogen.c
Normal file
35
energy_hydrogen.c
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@ -0,0 +1,35 @@
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#include "hydrogen.h"
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int main() {
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const double a[6] = {0.1, 0.2, 0.5, 1., 1.5, 2.};
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const int sizex = 50;
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double energy, r[3];
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double x[sizex], dx, w, wsum, dV;
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dx = 10.0 / (sizex - 1);
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for (int i = 0; i < sizex; ++i) {
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x[i] = -5.0 + (i - 1) * dx;
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}
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dV = dx * dx * dx;
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for (int l = 0; l < 6; ++l) {
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energy = 0.0;
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wsum = 0.0;
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for (int i = 0; i < sizex; ++i) {
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r[0] = x[i];
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for (int j = 0; j < sizex; ++j) {
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r[1] = x[j];
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for (int k = 0; k < sizex; ++k) {
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r[2] = x[k];
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w = psi(a[l], r, 3) * psi(a[l], r, 3) * dV;
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wsum += w;
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energy += w * e_loc(a[l], r, 3);
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}
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}
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}
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printf("a = %.2f E = %.5f \n", a[l], energy / wsum);
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}
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return 0;
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}
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@ -12,7 +12,7 @@ double potential(double *r, const int l) {
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if (pot > 0.0) {
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return -1.0 / sqrt(pot);
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}
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return -1;
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return 1e6;
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}
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73
qmc_metropolis.c
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73
qmc_metropolis.c
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@ -0,0 +1,73 @@
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#include "hydrogen.h"
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#include "qmc_stats.h"
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#include <stdlib.h>
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#include <time.h>
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void metropolis_montecarlo(double a, const int nmax, double dt,
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double *energy, double *accept) {
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int n_accept;
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double r_old[3], r_new[3], psi_old, psi_new, rnd;
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double aval, u;
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// Initial position
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for (int j = 0; j < 3; ++j) {
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rnd = (double) rand() / RAND_MAX;
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r_old[j] = dt * (2.0 * rnd - 1.0);
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}
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psi_old = psi(a, r_old, 3) * psi(a, r_old, 3);
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*energy = 0.0;
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*accept = 0.0;
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n_accept = 0;
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for (int i = 0; i < nmax; ++i) {
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// Compute and accumulate the local energy
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*energy += e_loc(a, r_old, 3);
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// Compute new position
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for (int j = 0; j < 3; ++j) {
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rnd = (double) rand() / RAND_MAX;
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r_new[j] = r_old[j] + dt * (2.0 * rnd - 1.0);
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}
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// New WF and acceptance probability
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psi_new = psi(a, r_new, 3) * psi(a, r_new, 3);
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aval = psi_new / psi_old;
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u = (double) rand() / RAND_MAX;
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if (u <= aval) {
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for (int j = 0; j < 3; ++j) {
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r_old[j] = r_new[j];
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}
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psi_old = psi_new;
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n_accept += 1;
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}
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}
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*energy /= nmax;
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*accept = (double) n_accept / nmax;
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}
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int main() {
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const double a = 1.2;
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const double dt = 1.0;
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const long nmax = 1e5;
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int nruns = 30;
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srand(time(NULL));
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double x[nruns], y[nruns], obs[2];
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for (int i = 0; i < nruns; ++i) {
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metropolis_montecarlo(a, nmax, dt, &x[i], &y[i]);
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}
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ave_error(x, nruns, obs);
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printf("E = %.5lf +/- %.5lf\n", obs[0], obs[1]);
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ave_error(y, nruns, obs);
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printf("A = %.5lf +/- %.5lf\n", obs[0], obs[1]);
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return 0;
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}
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27
qmc_stats.h
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27
qmc_stats.h
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@ -0,0 +1,27 @@
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#include <math.h>
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#include <stdio.h>
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void ave_error(double *x, const int n, double obs[2]) {
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// obs[1] --> mean and obs[2] --> err
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double var;
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if (n == 1) {
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obs[0] = x[0];
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obs[1] = 0.0;
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}
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else {
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for (int i = 0; i < n; ++i) {
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obs[0] += x[i];
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}
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obs[0] = obs[0] / n;
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var = 0.0;
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for (int i = 0; i < n; ++i) {
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var += (x[i] - obs[0]) * (x[i] - obs[0]);
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}
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var = var / (n - 1);
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obs[1] = sqrt(var / n);
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}
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}
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44
qmc_uniform.c
Normal file
44
qmc_uniform.c
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@ -0,0 +1,44 @@
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#include "hydrogen.h"
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#include "qmc_stats.h"
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#include <stdlib.h>
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#include <time.h>
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double uniform_montecarlo(double a, const int nmax) {
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double r[3], energy, norm, w, rnd;
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norm = 0.0;
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energy = 0.0;
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for (int i = 0; i < nmax; ++i) {
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for (int j = 0; j < 3; ++j) {
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rnd = (double) rand() / RAND_MAX;
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r[j] = -5.0 + 10.0 * rnd;
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}
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w = psi(a, r, 3) * psi(a, r, 3);
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norm += w;
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energy += w * e_loc(a, r, 3);
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}
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return energy / norm;
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}
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int main() {
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const double a = 1.2;
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const long nmax = 1e5;
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int nruns = 30;
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srand(time(NULL));
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double x[nruns], obs[2];
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for (int i = 0; i < nruns; ++i) {
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x[i] = uniform_montecarlo(a, nmax);
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}
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ave_error(x, nruns, obs);
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printf("E = %.5lf +/- %.5lf\n", obs[0], obs[1]);
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return 0;
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}
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41
variance_hydrogen.c
Normal file
41
variance_hydrogen.c
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@ -0,0 +1,41 @@
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#include "hydrogen.h"
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int main() {
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const double a[6] = {0.1, 0.2, 0.5, 1., 1.5, 2.};
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const int sizex = 50;
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double energy, r[3], sigma;
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double x[sizex], dx, w, wsum, dV, e_tmp;
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dx = 10.0 / (sizex - 1);
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for (int i = 0; i < sizex; ++i) {
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x[i] = -5.0 + i * dx;
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}
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dV = dx * dx *dx;
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for (int l = 0; l < 6; ++l) {
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energy = 0.0;
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sigma = 0.0;
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wsum = 0.0;
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for (int i = 0; i < sizex; ++i) {
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r[0] = x[i];
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for (int j = 0; j < sizex; ++j) {
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r[1] = x[j];
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for (int k = 0; k < sizex; ++k) {
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r[2] = x[k];
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w = psi(a[l], r, 3) * psi(a[l], r, 3) * dV;
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wsum += w;
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e_tmp = e_loc(a[l], r, 3);
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energy += w * e_tmp;
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sigma += w * e_tmp * e_tmp;
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}
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}
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}
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energy = energy / wsum;
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sigma = sigma / wsum;
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sigma -= energy * energy;
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printf("a = %.2lf E = %.5lf Sigma^2 = %.5lf\n", a[l], energy, sigma);
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}
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return 0;
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}
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@ -4,6 +4,8 @@ import numpy as np
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from hydrogen import e_loc, psi
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interval = np.linspace(-5,5,num=50)
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print(interval
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)
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delta = (interval[1]-interval[0])**3
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@ -34,5 +36,5 @@ for a in [0.1, 0.2, 0.5, 0.9, 1., 1.5, 2.]:
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E = E / norm
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E2 = E2 / norm
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s2 = E2 - E**2
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s2 = E2 #- E**2
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print(f"a = {a} \t E = {E:10.8f} \t \sigma^2 = {s2:10.8f}")
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