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Journal of Physics A Mathematical and General

Some comments on: the Kim-Sukhatme alternative approach to nonrelativistic perturbation theory

Harry A. Mavromatis

Published Jun 21, 1993• 2 citations
Publisher

Abstract

The new perturbation theory expressions obtained by Kim and Sukhatme (1992) are commented on, and some new results are obtained starting from their expressions.
DOI
10.1088/0305-4470/26/12/006

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Comments on `The Dalgarno - Lewis method as a perturbation theory' by Nandiet al(1996J. Phys. A: Math. Gen.291101) and on `Alternate approach to non-relativistic perturbation theory' by Kim and Sukhatme (1992J. Phys. A: Math. Gen.25L647)

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Harry A. Mavromatis

The perturbation theory expressions obtained by Kim and Sukhatme [\lq\lq Alternative approach to non-relativistic perturbation theory", J. Phys. A 25 (1992) L647-L650] are compared with the results of the LPT formalism, developed by Aharanov and Au [\lq\lq New approach to perturbation theory", Phys. Rev. Lett. 42 (1979) 1582-1585, and subsequent papers]. The step by step connection between the two formalisms is shown and commented on, and an illustrative example is given.

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Logarithmic perturbation expansions in nonrelativistic quantum mechanics

Tom D. Imbo, U. Sukhatme

We discuss an alternative method of performing coupling constant perturbation expansions in nonrelativistic quantum mechanics. This method, called logarithmic perturbation theory, yields new expressions for any-order corrections En to an unperturbed bound-state energy which do not involve cumbersome sums over intermediate unperturbed states. In one dimension, these corrections En can be evaluated using a simple explicit form containing a small number of integrals. In more than one dimension the approach is systematic but computations require the solution of well-defined partial differential equations. For order n=2 this equation is identical to that appearing in the method of Dalgarno and Lewis. Numerous illustrative examples are presented.

American Journal of Physics•Feb 1, 1984•44 citations
We discuss an alternative method of performing coupling constant perturbation expansions in nonrelativistic quantum mechanics. This method, called logarithmic perturbation theory, yields new expressions for any-order corrections En to an unperturbed bound-state energy which do not involve cumbersome sums over intermediate unperturbed states. In one dimension, these corrections En can be evaluated using a simple explicit form containing a small number of integrals. In more than one dimension the approach is systematic but computations require the solution of well-defined partial differential equations. For order n=2 this equation is identical to that appearing in the method of Dalgarno and Lewis. Numerous illustrative examples are presented.