Improvements to the computation of eigenvalues and eigenfunctions of two-dimensional Schrödinger equations by constant perturbation based algorithms

We present important improvements and additions to a modern technique developed by Ixaru to solve the time-dependent two-dimensional Schrödinger equation with homogeneous Dirichlet boundary conditions over a rectangular domain. The algorithm, first described in Ixaru (2010), is based on the so-calle...

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Bibliographic Details
Published in:	Journal of computational and applied mathematics Vol. 412; p. 114292
Main Authors:	Baeyens, Toon, Van Daele, Marnix
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.10.2022
Subjects:	Constant Perturbations Methods Eigenfunctions Eigenvalues Schrödinger equation Eigenvalues Eigenfunctions Constant Perturbations Methods Schrödinger equation
ISSN:	0377-0427, 1879-1778
Online Access:	Get full text
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Summary:	We present important improvements and additions to a modern technique developed by Ixaru to solve the time-dependent two-dimensional Schrödinger 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.
ISSN:	0377-0427 1879-1778
DOI:	10.1016/j.cam.2022.114292