A numerical algorithm for solving the coupled Schrödinger equations using inverse power method

The inverse power method is a numerical algorithm to obtain the eigenvectors of a matrix. In this work, we develop an iteration algorithm, based on the inverse power method, to numerically solve the Schrödinger equation that couples an arbitrary number of components. Such an algorithm can also be ap...

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Bibliographic Details
Published in:	Computer physics communications Vol. 303; p. 109284
Main Authors:	Zhao, Jiaxing, Shi, Shuzhe
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.10.2024
Subjects:	Coupled Schrödinger-like equations Eigenvalue and eigenstate Inverse power method Inverse power method Coupled Schrödinger-like equations Eigenvalue and eigenstate
ISSN:	0010-4655, 1879-2944
Online Access:	Get full text
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Summary:	The inverse power method is a numerical algorithm to obtain the eigenvectors of a matrix. In this work, we develop an iteration algorithm, based on the inverse power method, to numerically solve the Schrödinger equation that couples an arbitrary number of components. Such an algorithm can also be applied to the multi-body systems. To show the power and accuracy of this method, we also present an example of solving the Dirac equation under the presence of an external scalar potential and a constant magnetic field, with source code publicly available.
ISSN:	0010-4655 1879-2944
DOI:	10.1016/j.cpc.2024.109284