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import pytest
import numpy as np
import matplotlib.pyplot as plt
from schroedinger import (
Config, potential_interp, build_potential, solve_schroedinger
)
def psi(x, n, a):
n += 1 # Index starting from 0
x = -x + a / 2 # Reflect x and move to the left
return np.sqrt(2 / a) * np.sin(n * np.pi * x / a)
def energy(n, a, m):
return (n + 1)**2 * np.pi**2 / m / a**2 / 2.0
def test_infinite():
conf = Config('test/infinite.inp')
potential, delta = build_potential(conf)
e, v = solve_schroedinger(conf.mass, potential[:, 1], delta, conf.eig_interval)
# Account for -v also being an eigenvector if v is one
v = np.abs(v)
a = np.abs(conf.points[1][0] - conf.points[0][0])
e_theory = np.zeros(e.shape)
v_theory = np.zeros(v.shape)
for n in range(e.shape[0]):
e_theory[n] = energy(n, a, conf.mass)
v_theory[:, n] = np.abs(psi(potential[:, 0], n, a))
# for n in range(e.shape[0]):
# plt.plot(potential[:, 0], np.abs(v[:, n]), label='Num{}'.format(n))
# plt.plot(potential[:, 0], np.abs(v_theory[:, n]), ls='--', label='Theory{}'.format(n))
# plt.legend()
# plt.savefig('test.pdf')
assert (np.allclose(e, e_theory, rtol=1e-2, atol=1e-2)
and np.allclose(v, v_theory, rtol=1e-2, atol=1e-2))
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