Exact and quasi-exact solvability of two-dimensional superintegrable quantum systems. I. Euclidean space

2004/12/11 by E. G. Kalnins, Kalnins, E. G., W. Miller Jr. +3
Mathematics · Physics and Astronomy · #35Q40 #81Q05 #81R12 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:35Q40 #msc:81Q05 #msc:81R12

paper · pdf · doi:10.48550/arxiv.math-ph/0412035

36 pages

arxiv created 2004/12/11 · arxiv updated 2009/12/01

Abstract

In this article we show that separation of variables for second-order superintegrable systems in two-dimensional Euclidean space generates both exactly solvable (ES) and quasi-exactly solvable (QES) problems in quantum mechanics. In this article we propose the another definition of ES and QES. The quantum mechanical problem is called ES if the solution of Schroedinger equation, can be expressed in terms of hypergeometrical functions _mF_n and is QES if the Schroedinger equation admit polynomial solutions with the coefficients satisfying the three-term or more higher order of recurrence relations

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