Arbitrary l-wave bound states of the Schrödinger equation for the hyperbolical molecular potential

Within the framework of supersymmetric quantum mechanics method, we study by an algebraic method the arbitrary l-wave bound states of the Schrodinger equation for the hyperbolical molecular potential by a proper approximation to nonlinear centrifugal term. The explicitly analytical formula of energy levels is derived, and the corresponding bound state wave functions are presented. The function analysis method is used to rederive the same energy levels of the quantum system under consideration to check the validity of this algebraic method. In addition, it is shown from numerical results of energy levels that above certain α parameter depending on the choices of potential parameters V1 and V2 the hyperbolical molecular potential cannot trap a particle as it becomes weaker and the energy level starts to turn positive when the potential parameter α becomes larger. © 2014 Wiley Periodicals, Inc.