kees-study/cds-numerical-methods
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

11: Switch to Riemann midpoint sums and comment on that

Browse Source
This commit is contained in:
Kees van Kempen
2022-03-17 14:19:59 +01:00
parent f97dea859b
commit f7ac2c3ff7
1 changed files with 4 additions and 4 deletions
Download Patch File Download Diff File Expand all files Collapse all files

8
Week 6/11 Parabolic PDEs: 1D Schrödinger Equation with Potential.ipynb
View File

@ -259,7 +259,7 @@
"text": [ "text": [
"Eigenstate n = 0 yields total probability mass = 0.9999999999999999\n", "Eigenstate n = 0 yields total probability mass = 0.9999999999999999\n",
"Eigenstate n = 1 yields total probability mass = 1.0\n", "Eigenstate n = 1 yields total probability mass = 1.0\n",
"Eigenstate n = 2 yields total probability mass = 0.9999999999999997\n", "Eigenstate n = 2 yields total probability mass = 1.0\n",
"Eigenstate n = 3 yields total probability mass = 1.0\n" "Eigenstate n = 3 yields total probability mass = 1.0\n"
] ]
}, },
@ -286,9 +286,9 @@
"fig = plt.figure(figsize=(12,12))\n", "fig = plt.figure(figsize=(12,12))\n",
"\n", "\n",
"for n in range(the_first_few):\n", "for n in range(the_first_few):\n",
" # TODO: Should SEQStat return normalized eigenfunctions? \n", " # TODO: Should SEQStat return normalized eigenfunctions?\n",
" # Normalize the found eigenfunctions\n", " # Normalize the found eigenfunctions using Riemann midpoint sums\n",
" prob_mass = np.sum((x[1:] - x[:-1])*Psi[:-1, n]**2)\n", " prob_mass = np.sum((x[1:] - x[:-1])*(Psi[1:, n]**2 + Psi[:-1, n]**2)/2)\n",
" Psi[:, n] /= np.sqrt(prob_mass)\n", " Psi[:, n] /= np.sqrt(prob_mass)\n",
" \n", " \n",
" # Confirm normalization\n", " # Confirm normalization\n",