Application of Grimm-Storer Diffusion Approximation Method to Schrödinger Equation With Short Range Potential in One Dimension

Abstract

In this research we consider a system of one particle moving under the influence of short range potential. The applicability of solving Schrödinger equation by the method of diffusion due to Grimm-Storer approximation for a short range potential is investigated. Schrödinger equation can be solved to get the ground state and first excited state wave function and their Eigenvalues using other methods, like the finite difference method and in some cases the analytic solution if available. Both methods were used to compare solutions to that derived by the diffusion approximation method. In this study an exponential and a square well potential are taken as examples.