PySlise : a Python package for solving Schrödinger equations

Abstract

This is an introduction to a new Python package that is able to solve numerically the one and two-dimensional time independent Schrödinger equation. Accompanying this package there is a web based GUI. The main motivator of this research is modernizing and bringing together existing techniques and proven methods. Matslise is a very effective implementation of CP-methods for the one-dimensional Sturm-Liouville equation. But due to the numerous features, this implementation is not highly optimised for efficiency. For this reason we have reimplemented and optimised the algorithms of Matslise and Matscs in C++. This reimplementation became the computation engine for the Python package and the web based GUI (WebAssembly). The Python package is less feature-rich than the original Matslise and Matscs (only Schrödinger equation, no degenerate case detection...), but a lot more optimised. These optimisations include: very efficient eigenfunction calculations, smarter backward propagation, higher order method for Matscs, on request error calculation, using C++ with Eigen. On top of that there is a unified interface to communicate with Matslise, Matscs and the new code for the two-dimensional case