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arXiv:quant-ph/0011116

The Relaxation Method for Solving the Schrodinger Equation in Configuration Space with the Coulomb and Linear Potentials

Alfred Tang, Daniel R. Shillinglaw, George Nill

Published Nov 29, 2000• 0 citations
arXivHTMLPDF

Abstract

The non-relativistic Schrodinger equation with the linear and Coulomb potentials is solved numerically in configuration space using the relaxation method. The numerical method presented in this paper is a plain explicit Schrodinger solver which is conceptually simple and is suitable for advanced undergraduate research.
DOI
10.48550/arxiv.quant-ph/0011116

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A method of solving the Schrödinger equation based on the use of constant particle-particle interaction potential surfaces (IPS) is proposed. The many-body wave function is presented in a configuration interaction form, with coefficients depending on the total interaction potential. The corresponding set of linear ordinary differential equations for the coefficients was developed. To reduce the computational work, a hierarchy of approximations based on interaction potential surfaces of a part of the particle system was worked out. The solution of a simple exactly solvable model and He-like ions proves that this method is more accurate than the conventional configuration interaction method and demonstrates a better convergence with a basis set increase.
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