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'''
Test solutions to the infinite potential well by comparing with theoretical
values
'''
import numpy as np
from numpy.typing import NDArray
from schroedinger import (
Config, build_potential, solve_schroedinger
)
def psi(x: NDArray[np.float64], level: int, resolution: float) -> NDArray[np.float64]:
'''Generate the n=level wave function'''
level += 1 # Index starting from 0
x = -x + resolution / 2 # Reflect x and move to the left
return np.sqrt(2 / resolution) * np.sin(level * np.pi * x / resolution)
def energy(level: int, resolution: float, mass: float) -> float:
'''Energy eigenvalue for the n=level wave function'''
return (level + 1)**2 * np.pi**2 / mass / resolution**2 / 2.0
def test_infinite() -> None:
'''Test infinite potential well'''
conf = Config('test/infinite.inp')
potential, delta = build_potential(conf)
energies, wavefuncs = solve_schroedinger(conf.mass, potential[:, 1], delta,
conf.eig_interval)
# Account for -v also being an eigenvector if v is one
wavefuncs = np.abs(wavefuncs)
resolution = np.abs(conf.points[1][0] - conf.points[0][0])
energies_theory = np.zeros(energies.shape)
wavefuncs_theory = np.zeros(wavefuncs.shape)
for level in range(energies.shape[0]):
energies_theory[level] = energy(level, resolution, conf.mass)
wavefuncs_theory[:, level] = np.abs(psi(potential[:, 0], level,
resolution))
assert (np.allclose(energies, energies_theory, rtol=1e-2, atol=1e-2)
and np.allclose(wavefuncs, wavefuncs_theory, rtol=1e-2, atol=1e-2))
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