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The Finite-Difference Time-Domain (FDTD) method is a well-known technique forthe analysis of quantum devices. It solves a discretized Schrodinger equationin an explicitly iterative process. However, the method requires the spatialgrid size and time step satisfy a very restricted condition in order to preventthe numerical solution from diverging. In this article, we present ageneralized FDTD (G-FDTD) method for solving the multi-dimensionaltime-dependent Schrodinger equation, and obtain a more relaxed condition forstability when the finite difference approximations for spatial derivatives areemployed. As such, a larger time step may be chosen. This is particularlyimportant for quantum computations. The new G-FDTD method is tested bysimulation of a particle moving in 2-D free space and then hitting an energypotential. Numerical results coincide with those obtained based on thetheoretical analysis.

A G-FDTD Method for Solving the Multi-Dimensional Time-Dependent Schrodinger Equation