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Advances in High Energy Physics
Volume 2017 (2017), Article ID 8429863, 13 pages
Research Article

Exact Solutions of a Class of Double-Well Potentials: Algebraic Bethe Ansatz

Department of Physics, University of Guilan, Rasht 41635-1914, Iran

Correspondence should be addressed to M. Baradaran

Received 5 September 2017; Revised 15 November 2017; Accepted 19 November 2017; Published 26 December 2017

Academic Editor: Marc de Montigny

Copyright © 2017 M. Baradaran and H. Panahi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


Applying the Bethe ansatz method, we investigate the Schrödinger equation for the three quasi-exactly solvable double-well potentials, namely, the generalized Manning potential, the Razavy bistable potential, and the hyperbolic Shifman potential. General exact expressions for the energies and the associated wave functions are obtained in terms of the roots of a set of algebraic equations. Also, we solve the same problems using the Lie algebraic approach of quasi-exact solvability through the algebraization and show that the results are the same. The numerical evaluation of the energy spectrum is reported to display explicitly the energy levels splitting.