International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 358198, 9 pages
doi:10.1155/2011/358198
Research Article

Quasi-Exact Solvability of a Hyperbolic Intermolecular Potential Induced by an Effective Mass Step

Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, IN 46408, USA

Received 3 December 2010; Accepted 11 January 2011

Academic Editor: N. Govil

Copyright © 2011 Axel Schulze-Halberg. 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.

Abstract

It is shown that a nonsolvable third-order hyperbolic potential becomes quasi-exactly solvable after the introduction of a hyperbolic effective mass step. Stationary energies and L2-solutions of the corresponding Schrödinger equation are obtained in explicit form.