Pyslise

Pyslise [1] is a collection of algorithms to solve one (and two, in development) dimensional time-independent Schrödinger equations. These algorithms are based upon constant perturbation methods to efficiently solve these eigenvalue problems.

The code (and name) is based on Matslise [2]. This is a feature-rich MATLAB library for solving the one dimensional time independent Schrödinger equation.

To solve the two dimensional problem an algorithm is developed on the basis of a method proposed by Ixaru [3].

This implementation is developed in C++ with a focus on efficiency. This code is precompiled and packaged in wheels for 64 bit Linux, Windows, and Mac.

Documentation

Full documentation can be found on matslise.ugent.be. This document contains some examples of how to use this library.

On the same page an interactive version is available.

Examples

One dimensional problems can be tackled with:

from pyslise import Pyslise
from math import pi, cos

problem = Pyslise(lambda x: 2*cos(2*x), 0, pi, tolerance=1e-6)
problem.eigenvaluesByIndex(0, 10, (0, 1), (0, 1))

Also two dimensional problems are possible:

from pyslise import Pyslise2D

def V(x, y):
    return (1 + x**2) * (1 + y**2)

problem = Pyslise2D(V, -5.5,5.5, -5.5,5.5, tolerance=1e-6)
problem.eigenvalues(0,13)

Bibliography

• [1] Baeyens, Toon, and Marnix Van Daele. “The Fast and Accurate Computation of Eigenvalues and Eigenfunctions of Time-Independent One-Dimensional Schrödinger Equations.” Computer Physics Communications, August 26, 2020, 107568. https://doi.org/10.1016/j.cpc.2020.107568.
• [2] Ledoux, Veerle, and Marnix Van Daele. “MATSLISE 2.0 : A Matlab Toolbox for Sturm-Liouville Computations.” ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 42, no. 4 (2016): 18.
• [3] Ixaru, L. Gr. “New Numerical Method for the Eigenvalue Problem of the 2D Schrödinger Equation.” Computer Physics Communications 181 (October 1, 2010): 1738–42. https://doi.org/10.1016/j.cpc.2010.06.031.