Solutions of N-dimensional Schrödinger equation with Morse potential via Laplace transforms

Abstract

A study is undertaken to investigate an analytical solution for the N-dimensional Schrödinger equation with the Morse potential based on the Laplace transformation method. The results show that in the Pekeris approximation, the radial part of the Schrödinger equation reduces to the corresponding equation in one dimension. Hence its exact solutions can be obtained by the Laplace transformation method of G. Chen, phys. Lett. A 326 (2004) 55. In addition, a comparison is made between the energy spectrum resulted from this method and the spectra that are obtained from the two-point quasi-rational approximation method and the Nikiforov-Uvarov approach.

Solutions of Morse potential with position-dependent mass by Laplace transform

“…Fig. 1a, exactly coincides with the diagram has already been obtained for the constant mass problem [43]. Fig.…”

“…This case exactly corresponds to the constant mass case and for which we put G ¼ À2kF and s ¼ 1. This case has already been studied in [43], and we show that its solutions coincides with the results in the next section as well. The other possible set of the appropriate parameters have the following forms:…”

“…(29), [40,43]. By applying Laplace transform FðsÞ ¼ L ½f ðyÞ ¼ R 1 0 e Àsy f ðyÞdy, [35], the following equation can be obtained…”

“…It was Schrödinger who used this technique for the first time in quantum physics to solve the radial eigenfunction of hydrogen atom [36]. The method has become commonly employed ever since to solve various kind of the spherically symmetric potentials [37][38][39][40][41][42][43][44].…”

“…In this way, we can suitably separate the terms contained the mass function from the terms of the field derivatives. Then, by applying some simple constraints, on the terms included the mass function, we construct the mass function in such a way that the corresponding equation can be solved via the Laplace transformation method of [40,43]. The organization of this paper is as follows: In section two, we first introduce the initial form of the mass function with undetermined parameters.…”