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Advances in High Energy Physics
Volume 2017, Article ID 2181532, 8 pages
Research Article

Lie Symmetry and the Bethe Ansatz Solution of a New Quasi-Exactly Solvable Double-Well Potential

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

Correspondence should be addressed to H. Panahi;

Received 4 November 2016; Revised 14 January 2017; Accepted 24 January 2017; Published 2 March 2017

Academic Editor: Akpan Ikot

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.


We study the Schrödinger equation with a new quasi-exactly solvable double-well potential. Exact expressions for the energies, the corresponding wave functions, and the allowed values of the potential parameters are obtained using two different methods, the Bethe ansatz method and the Lie algebraic approach. Some numerical results are reported and it is shown that the results are in good agreement with each other and with those obtained previously via a different method.