Abstract
We present important improvements and additions to a modern technique developed by Ixaru to solve the time-dependent two-dimensional Schrodinger equation with homogeneous Dirichlet boundary conditions over a rectangular domain. The algorithm, first described in Ixaru (2010), is based on the so-called Constant Perturbation technique. In this paper, we refine and extend the algorithm with important features. We focus in particular on new algorithms for the determination of the index of the eigenvalues, for the orthonormalization of eigenfunctions, for automatic step size selection and for the accurate computation of integrals. We provide the new developments with sufficient theoretical background and numerical experiments. (c) 2022 Elsevier B.V. All rights reserved.
NSTL
Elsevier