Unified derivation of exact solutions for a class of quasi-exactly solvable models

Agboola, Davids and Zhang, Yao-Zhong (2012) Unified derivation of exact solutions for a class of quasi-exactly solvable models. Journal of Mathematical Physics, 53 4: . doi:10.1063/1.3701833

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Author Agboola, Davids
Zhang, Yao-Zhong
Title Unified derivation of exact solutions for a class of quasi-exactly solvable models
Journal name Journal of Mathematical Physics   Check publisher's open access policy
ISSN 0022-2488
Publication date 2012-04-09
Year available 2012
Sub-type Article (original research)
DOI 10.1063/1.3701833
Open Access Status File (Publisher version)
Volume 53
Issue 4
Total pages 13
Place of publication College Park, MD, United States
Publisher American Institute of Physics
Collection year 2013
Language eng
Formatted abstract
We present a unified treatment of exact solutions for a class of four quantum mechanical models, namely, the anharmonic singular potential, the generalized quantum isotonic oscillator, the soft-core Coulomb potential, and the non-polynomially modified oscillator. We show that all four cases are reducible to the same basic ordinary differential equation, which is quasi-exactly solvable. A systematic and closed form solution to the basic equation is obtained via the Bethe ansatz method. Using the result, general exact expressions for the energies and the allowed potential parameters are given explicitly for each of the four cases in terms of the roots of a set of algebraic equations. A hidden sl(2) algebraic structure is also discovered in these models.
Keyword Algebra
Differential equations
Harmonic oscillators
Quantum theory
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published online 9 April 2012

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2013 Collection
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Citation counts: TR Web of Science Citation Count  Cited 22 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 20 times in Scopus Article | Citations
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