Stability of Finite Difference Solution of Time-Dependent Schrodinger Equations
E. O. Ohwadua *
Department of Mathematical Sciences, Bingham University, Nasarawa State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, the stability of finite difference methods for time-dependent Schrodinger equation with Dirichlet boundary conditions on a staggered mesh was considered with explicit and implicit discretization. Using the matrix representation for the numerical algorithm, it is shown that for the explicit finite difference method, the solution is conditionally stable while it becomes unconditionally stable for implicit finite difference methods. A 1D Harmonic Oscillator problem shall be used to illustrate this behaviour.
Keywords: Schrodinger equation, finite difference, discretization, dirichlet boundary conditions, crank-nicolson.