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11: Switch to Riemann midpoint sums and comment on that

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Kees van Kempen
2022-03-17 14:19:59 +01:00
parent f97dea859b
commit f7ac2c3ff7
1 changed files with 4 additions and 4 deletions
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8
Week 6/11 Parabolic PDEs: 1D Schrödinger Equation with Potential.ipynb
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@ -259,7 +259,7 @@
"text": [
"Eigenstate n = 0 yields total probability mass = 0.9999999999999999\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"
]
},
@ -286,9 +286,9 @@
"fig = plt.figure(figsize=(12,12))\n",
"\n",
"for n in range(the_first_few):\n",
" # TODO: Should SEQStat return normalized eigenfunctions? \n",
" # Normalize the found eigenfunctions\n",
" prob_mass = np.sum((x[1:] - x[:-1])*Psi[:-1, n]**2)\n",
" # TODO: Should SEQStat return normalized eigenfunctions?\n",
" # Normalize the found eigenfunctions using Riemann midpoint sums\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",
" \n",
" # Confirm normalization\n",