A Python package for solving the one-particle Schroedinger equation on any dimension using Numpy and Scipy
This was done for a research project but should be of general enough usefulness, though still not well documented. It provides at the moment two basis sets, plane waves and direct space with a Numerov inspired integration method. References to the Matrix Numerov method used can be found here for the 1D case and a full description of the method in N dimensions is available here.
For a basic usage example, this script will produce the eigen energies for a proton in a harmonic potential of constant k = 2 eV/Angstrom.
import numpy as np
import scipy.constants as cnst
from pyschro.solve import QSolution
k = 2 # eV/Ang^2
def V(r):
return (2*1e20*cnst.electron_volt)*np.linalg.sum(r**2, axis=-1)
sol = QSolution([[-3e-10, 3e-10]], # Bounds: array of N pairs, one for each dimension, in meters
300, # Grid points
V, # Potential function: takes a (grid, N) array in meters, returns a (grid,) one in J
cnst.m_p) # Mass in kg; here a proton
# Default basis set is direct space
print 'Eigenvalues: '
for i, e in enumerate(sol.evals):
print 'n = {0}, E = {1} eV'.format(i+1, e/cnst.electron_volt)