On the feasibility of analytical approximations for the bound state energy spectra of one-dimensional quantum systems

Abstract

Finding the bound state energy spectra for one-dimensional quantum systems generally involves the solution of transcendental equations. In this paper we modify an approach recently introduced by Bonfim and Griffiths for obtaining approximate expressions for the eigenenergies of one-dimensional quantum systems. The modification entails the addition of a small corrective term as used in a symbolic Newton method. The accuracy of the modified approach as compared to the Bonfim-Griffiths approach is investigated in the context of a particle in a finite square well potential. Analytical approximations for the eigenenergies are also obtained for the delta-function in an infinite square well potential, and the double delta-function potential.