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August 4, 2025 05:53
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"id": "1496ec94-0fdf-42f8-a638-a00b67e75351", | |
"metadata": {}, | |
"source": [ | |
"# Momentum Eigenstates in 1D" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 15, | |
"id": "f9ed4cfc-b8ab-47f4-89cd-abb43a6a316d", | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import numpy as np\n", | |
"from numpy.linalg import eigh\n", | |
"import matplotlib.pyplot as plt" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 16, | |
"id": "0a6785b4-3586-45c1-b487-552204d982d9", | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"# Define some constants\n", | |
"\n", | |
"M_E: float = 1.0 # Mass of the particle\n", | |
"N: int = 512 # Discretization size\n", | |
"L: float = 512.0 # Size of the simulation domain\n", | |
"# Momentum\n", | |
"P: np.ndarray = N*np.fft.fftfreq(N)*2.0*np.pi/L\n", | |
"# Spatial step\n", | |
"DX: float = L/N\n", | |
"# Position\n", | |
"X: np.ndarray = np.linspace(0.0, L - DX, N)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 17, | |
"id": "b98963c7-e430-4b1b-acd7-6292a04ea3fa", | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"# Harmonic oscillator potential\n", | |
"OMEGA: float = 0.001\n", | |
"V: np.ndarray = OMEGA**2*(X - L/2.0)**2/2.0\n", | |
"\n", | |
"# V: np.ndarray = 0.01*(np.cos(2.0*np.pi*X/L) + 1.0)\n", | |
"# V: np.ndarray = 0.01*(X/L)\n", | |
"# V: np.ndarray = np.where(np.abs((X - L/2.0)/L) < 0.25, 0.0, 0.01)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "b3e70ce4-ec19-4163-a0ab-663552056a10", | |
"metadata": {}, | |
"source": [ | |
"In momentum space, the Hamiltonian $H$ can be expressed as\n", | |
"$$ <p_1|H|p_2> = <p_1|\\frac{p^2}{2m}|p_2> + <p_1|V|p_2>,$$\n", | |
"Where $<p_1|$ and $|p_2>$ are momenta basis vector bra-kets, $\\frac{p^2}{2m}$ is the kinetic energy matrix, and $V$ is the potential operator. Here $\\frac{p^2}{2m}$ is diagonal. On the other hand, the elements of the operator $V$ are\n", | |
"$$<p_1|V|p_2> = \\int <p_1|x_1> (\\int <x_1|V|x_2><x_2|p_2> dx_2) dx_1,$$\n", | |
"where various position basis identity resolutions have been inserted. Now $<x_1|V|x_2>$ is diagonal in position space; $\\int ... <x_2|p_2> dx_2 = \\int ... \\exp(-ip_2 x_2) dx_2$ gives the inverse Fourier transform from the $x_2$ basis to $p_2$; similarly $\\int <p_1|x_1> ... dx_1 = \\int \\exp(ip_1 x_1) ... dx_1$ takes the Fourier transform from $x_1$ to $p_1$.\n", | |
"\n", | |
"From these considerations, the discretized momentum space Hamiltonian $H$ is implemented with the following code:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 18, | |
"id": "7349fe38-577c-4577-a684-2734f4a0872a", | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"H: np.ndarray = np.diag(P**2/(2.0*M_E)) \\\n", | |
" + np.fft.fft(np.fft.ifft(np.diag(V), axis=1), axis=0)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "caf74f8c-33e8-458a-a6f9-cf836a520490", | |
"metadata": {}, | |
"source": [ | |
"It is helpful to plot this matrix:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 19, | |
"id": "5e8e9570-82e4-4a52-8a8c-af696526fb9b", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
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", | |
"text/plain": [ | |
"<Figure size 640x480 with 2 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.imshow(np.abs(H))\n", | |
"plt.title(\"Momentum space Hamiltonian matrix elements (absolute value)\")\n", | |
"plt.colorbar()\n", | |
"plt.show()\n", | |
"plt.close()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 20, | |
"id": "a87aaf1c-48c5-4f1f-b0e6-69a9d4b3af00", | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"energies, eigenstates = eigh(H)\n", | |
"ind_sort = np.argsort(energies)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 21, | |
"id": "fa0c3176-f8c4-4c80-be47-a2ab5e9c293d", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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", | |
"text/plain": [ | |
"<Figure size 640x480 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"for i in range(4):\n", | |
" plt.plot([X[0], X[-1]], [energies[ind_sort[i]], energies[ind_sort[i]]],\n", | |
" color='black', alpha=0.5, linewidth=0.5)\n", | |
" plt.plot(X, 0.1*np.abs(np.fft.ifft(eigenstates.T[ind_sort[i]], norm='ortho')),\n", | |
" label=f\"$|\\psi_{i}(x)|$\")\n", | |
"plt.plot(X, V, color='black', linestyle='--', label='Potential V(x)')\n", | |
"plt.legend()\n", | |
"plt.xlabel('Position x (a.u.)')\n", | |
"plt.ylabel('Scaled $\\psi$ amplitude/energy value (a.u.)')\n", | |
"plt.title(\"Eigenstates\")\n", | |
"plt.show()\n", | |
"plt.close()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 22, | |
"id": "ecd7a9f1-b83b-45f6-9ba9-0c79b5bd8bdf", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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", | |
"text/plain": [ | |
"<Figure size 640x480 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.title('Energies')\n", | |
"plt.scatter(np.arange(0, N)[:N//5],\n", | |
" [energies[i] for i in ind_sort][:N//5], label='numerical', marker='_')\n", | |
"exact_energies = OMEGA*(np.arange(0, N) + 0.5)[:N//5]\n", | |
"plt.scatter(np.arange(0, N)[:N//5],\n", | |
" exact_energies, label='exact', marker='_')\n", | |
"plt.legend()\n", | |
"plt.show()\n", | |
"plt.close()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"id": "2e86c44a-8897-43fd-a59f-aed74a35f0e2", | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3 (ipykernel)", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.8.12" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 5 | |
} |
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