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Finish ps16-1

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orosmatthew 2024-04-09 11:51:14 -04:00
parent cae077e001
commit 38ddca0596
1 changed files with 20 additions and 15 deletions
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19
ps16-1.py
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@ -1,12 +1,12 @@
import numpy as np import numpy as np
import pylab as pl import pylab as pl
a = 5 a = 10
D = 1 D = 1
hbar = 1 hbar = 1
m = 1 m = 1
z = 2.851 zs = np.array([5.963, 2.851, 1.745, 1.124])
l = z / a l = zs / a
V0 = 2 V0 = 2
@ -14,26 +14,31 @@ def cot(x):
return 1 / np.tan(x) return 1 / np.tan(x)
x = np.linspace(-10, 10, 1000) x = np.linspace(-20, 20, 1000)
x_pos = x[x > 0] x_pos = x[x > 0]
z0 = (a / hbar) * np.sqrt(2 * m * V0) z0 = (a / hbar) * np.sqrt(2 * m * V0)
print(f'z0 = {z0}') print(f'z0 = {z0}')
k = -l * cot(l * a) k = -l * cot(l * a)
F = np.sin(l * a) / np.exp(-k * a) F = np.sin(l * a) / np.exp(-k * a)
psis = []
for (i, z) in enumerate(zs):
psi_conditions = [ psi_conditions = [
(0 < x_pos) & (x_pos <= a), (0 < x_pos) & (x_pos <= a),
(x_pos > a) (x_pos > a)
] ]
psi_funcs = [ psi_funcs = [
lambda x: D * np.sin(l * x), lambda x: D * np.sin(l[i] * x),
lambda x: F * np.exp(-k * x), lambda x: F[i] * np.exp(-k[i] * x),
] ]
psi_half = np.piecewise(x_pos, psi_conditions, psi_funcs) psi_half = np.piecewise(x_pos, psi_conditions, psi_funcs)
psi = np.concatenate((-np.flip(psi_half), psi_half)) psi = np.concatenate((-np.flip(psi_half), psi_half))
psis.append(psi)
V0_graph = np.piecewise(x, [(x < -a), (-a <= x) & (x <= a), (x > a)], [0, -V0, 0]) V0_graph = np.piecewise(x, [(x < -a), (-a <= x) & (x <= a), (x > a)], [0, -V0, 0])
pl.plot(x, psi) pl.rcParams['figure.dpi'] = 300
pl.plot(x, V0_graph) pl.plot(x, V0_graph)
for (i, psi) in enumerate(psis):
pl.plot(x, psi, label=f'psi_odd_{i} z={zs[i]}')
pl.show() pl.show()