Solutions of N-dimensional Schr\"{o}dinger Equation with Morse Potential Via Laplace Transforms

A study is undertaken to investigate an analytical solution for the N-dimensional Schrodinger equation with the Morse potential based on the Laplace transformation method. The results show that in the Pekeris approximation, the radial part of the Schrodinger 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.