46 lines
948 B
Python
46 lines
948 B
Python
import numpy as np
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import pylab as pl
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a = 10
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D = 1
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hbar = 1
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m = 1
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zs = np.array([2.991, 5.98, 8.96, 11.927])
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l = zs / a
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V0 = 2
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def cot(x):
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return 1 / np.tan(x)
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x = np.linspace(-20, 20, 1000)
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x_pos = x[x > 0]
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z0 = (a / hbar) * np.sqrt(2 * m * V0)
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print(f'z0 = {z0}')
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k = -l * cot(l * a)
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F = np.sin(l * a) / np.exp(-k * a)
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psis = []
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for (i, z) in enumerate(zs):
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psi_conditions = [
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(0 < x_pos) & (x_pos <= a),
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(x_pos > a)
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]
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psi_funcs = [
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lambda x: D * np.sin(l[i] * x),
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lambda x: F[i] * np.exp(-k[i] * x),
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]
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psi_half = np.piecewise(x_pos, psi_conditions, psi_funcs)
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psi = np.concatenate((-np.flip(psi_half), psi_half))
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psis.append(psi)
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V0_graph = np.piecewise(x, [(x < -a), (-a <= x) & (x <= a), (x > a)], [0, -V0, 0])
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pl.rcParams['figure.dpi'] = 300
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pl.plot(x, V0_graph)
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for (i, psi) in enumerate(psis):
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pl.plot(x, psi, label=f'psi_odd_{i} z={zs[i]}')
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pl.legend()
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pl.show()
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