On the solvability of the generalized hyperbolic double-well models

Agboola, Davids (2014) On the solvability of the generalized hyperbolic double-well models. Journal of Mathematical Physics, 55 5: . doi:10.1063/1.4878118

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Author Agboola, Davids
Title On the solvability of the generalized hyperbolic double-well models
Journal name Journal of Mathematical Physics   Check publisher's open access policy
ISSN 0022-2488
1089-7658
1527-2427
Publication date 2014-05-01
Year available 2014
Sub-type Article (original research)
DOI 10.1063/1.4878118
Open Access Status File (Publisher version)
Volume 55
Issue 5
Total pages 8
Place of publication College Park, MD, United States
Publisher American Institute of Physics
Language eng
Formatted abstract
We present exact solutions for the Schrödinger equation with the hyperbolic double-well potential Vqp(x)=−V0sinhp(αx)/coshq(αx) . We show that the model preserves a finite dimensional polynomial space for some p and q. Thus using the Bethe ansatz method, we obtain closed form expressions for the spectrum and wavefunction, as well as the allowed parameter for the class Vδp(x) , which is contrary to a report in a recent article [C. A. Downing, J. Math. Phys.54, 072101 (2013)]. We also discuss the hidden sl 2 algebraic structure of the class.
Keyword Differential operators
Potentials
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Article no. 052102 (2014)

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2015 Collection
 
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Citation counts: TR Web of Science Citation Count  Cited 3 times in Thomson Reuters Web of Science Article | Citations
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Created: Tue, 24 Jun 2014, 10:36:24 EST by System User on behalf of School of Mathematics & Physics