On a Stable and Consistent Finite Difference Scheme for a Time-Dependent Schrodinger Wave Equation in a Finitely Low Potential Well

Abstract

In this paper, a stable and consistent criterion to an explicit finite difference scheme for a time-dependent Schrodinger wave equation (TDSWE) was presented. This paper is a departure from the well-established time independent Schrodinger Wave Equation (SWE). To develop the stability criterion for the scheme, the Fourier series method of von Newmann was adopted, while in establishing the consistency property, the concise definition of the consistent scheme was applied. This research is carried out for a particular case of a finitely low potential well.

Keywords: Time-Dependent Schrodinger Wave Equation, Stability, Consistency, Finite Potential Well, Finite Difference.