Stability of Finite Difference Solution of Time-Dependent Schrodinger Equations
Journal of Advances in Mathematics and Computer Science · pp. 167–180 · Published 24 May 2023
10.9734/jamcs/2023/v38i71782Abstract
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.
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