Perturbative solutions of quantum mechanical problems by symbolic computation
type: Item
instance of: scholarly article
title: Perturbative solutions of quantum mechanical problems by symbolic computation
zbMATH Open document ID: 0712.65111
DOI: 10.1016/0021-9991(90)90258-3
author: T. C. Scott
author: R. A. Moore
author: Michael Monagan
author: G. Fee
author: Edward R. Vrscay
published in: Journal of Computational Physics
publication date: 1990-01-01T00:00:00Z
review text: Symbolic computation is an effective alternative to many existing calculational methods for obtaining quantitative results. It represents the next level beyond the digital calculator as an efficient extension of the critical human mind. In this 30-page paper the authors have shown that the second author's decoupling technique is useful to achieve approximate solutions to the one particle Dirac equation, which is an example to meaningfully check the power of the new approach for solving quantum mechanical problems by perturbation theory. Here the use of an infinite basis set is avoided and each coefficient of the perturbation series is arrived at in a closed form. The techniques presented can be applied to other situations also and illustrations are given to indicate that symbolic computation has a great future.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 35Q40
zbMATH DE Number: 4172333
zbMATH Keywords: Symbolic computation
zbMATH Keywords: decoupling technique
zbMATH Keywords: one particle Dirac equation
zbMATH Keywords: perturbation theory
zbMATH Keywords: perturbation series
describes a project that uses: Maple
MaRDI profile type: Publication
full work available at URL: 0021-9991(90)90258-3
OpenAlex ID: W1975078471
cites work: Q4072022
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cites work: The Factorization Method
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cites work: Dirac's Equation and the Spin-Spin Interactions of Two Electrons
description: scientific article; zbMATH DE number 4172333