Finite Difference Schemes for the Unsteady State Schrödinger Equation in Three Dimensions with Complex Variables
Abstract
Abstract: In this paper we introduce three finite difference schemes to solve the three dimensions unsteady Schrödinger equation. The finite difference scheme developed for this purpose are based on the (1, 7) fully explicit scheme, the (7, 7) Crank-Nicolson technique and fourth order compact scheme. The computational accuracy is demonstrated by comparing the results of these schemes. The results show that the compact fourth order finite difference scheme is more accurate than the other schemes.
Keywords
compact finite difference, three dimension Schrödinger equation, fourth order, time dependentMetrics