Quasi-exact solvability beyond the sl(2) algebraization

We present evidence to suggest that the study of one-dimensional quasi-exactly solvable (QES) models in quantum mechanics should be extended beyond the usual sl(2) approach. The motivation is twofold: We first show that certain quasi-exactly solvable potentials constructed with the sl(2) Liealgebrai...

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Bibliographic Details
Published inPhysics of atomic nuclei Vol. 70; no. 3; pp. 520 - 528
Main Authors Gómez-Ullate, D., Kamran, N., Milson, R.
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.03.2007
Subjects
Algebra
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
EXACT SOLUTIONS
HAMILTONIANS
Lie groups
ONE-DIMENSIONAL CALCULATIONS
POLYNOMIALS
POTENTIALS
QUANTUM MECHANICS
SL GROUPS
SPECTRA
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Summary:We present evidence to suggest that the study of one-dimensional quasi-exactly solvable (QES) models in quantum mechanics should be extended beyond the usual sl(2) approach. The motivation is twofold: We first show that certain quasi-exactly solvable potentials constructed with the sl(2) Liealgebraic method allow for a new larger portion of the spectrum to be obtained algebraically. This is done via another algebraization in which the algebraic Hamiltonian cannot be expressed as a polynomial in the generators of sl(2). We then show an example of a new quasi-exactly solvable potential which cannot be obtained within the Lie algebraic approach.
ISSN:1063-7788
1562-692X
DOI:10.1134/S1063778807030118