46 lines
1.1 KiB
Python
46 lines
1.1 KiB
Python
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import numpy as np
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import pylab as pl
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def ladder_plus(xs: np.ndarray, psi: np.ndarray) -> np.ndarray:
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dx = xs[1] - xs[0]
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return -np.gradient(psi, dx) + xs * psi
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def ladder_minus(xs: np.ndarray, psi: np.ndarray) -> np.ndarray:
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dx = xs[1] - xs[0]
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return np.gradient(psi, dx) + xs * psi
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def normalize(psi: np.ndarray) -> None:
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psi /= np.sqrt(np.sum(psi * np.conjugate(psi)))
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x_vals = np.linspace(-5, 5, 1000)
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psi_0 = np.exp(-x_vals ** 2)
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normalize(psi_0)
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psi_funcs = [psi_0]
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for i in range(1, 4):
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psi_next = ladder_plus(x_vals, psi_funcs[i - 1])
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normalize(psi_next)
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psi_funcs.append(psi_next)
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pl.rcParams['figure.dpi'] = 300
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fig, axs = pl.subplots(2, 2, tight_layout=True)
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fig.tight_layout(pad=2.0)
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axs[0, 0].plot(x_vals, psi_funcs[0])
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axs[0, 0].set_title('ψ0')
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axs[0, 0].grid()
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axs[0, 1].plot(x_vals, psi_funcs[1], 'tab:orange')
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axs[0, 1].set_title('ψ1')
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axs[0, 1].grid()
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axs[1, 0].plot(x_vals, psi_funcs[2], 'tab:green')
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axs[1, 0].set_title('ψ2')
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axs[1, 0].grid()
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axs[1, 1].plot(x_vals, psi_funcs[3], 'tab:red')
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axs[1, 1].set_title('ψ3')
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axs[1, 1].grid()
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pl.show()
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