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

TL;DR

This paper introduces a generalized FDTD method for solving the multi-dimensional time-dependent Schrödinger equation, allowing larger time steps and improved stability for quantum simulations.

Contribution

A novel G-FDTD method that relaxes stability constraints, enabling more efficient and stable quantum device simulations compared to traditional FDTD approaches.

Findings

Numerical results match theoretical predictions.

The method allows larger time steps without divergence.

Enhanced stability for multi-dimensional quantum simulations.

Abstract

The Finite-Difference Time-Domain (FDTD) method is a well-known technique for the analysis of quantum devices. It solves a discretized Schrodinger equation in an explicitly iterative process. However, the method requires the spatial grid size and time step satisfy a very restricted condition in order to prevent the numerical solution from diverging. In this article, we present a generalized FDTD (G-FDTD) method for solving the multi-dimensional time-dependent Schrodinger equation, and obtain a more relaxed condition for stability when the finite difference approximations for spatial derivatives are employed. As such, a larger time step may be chosen. This is particularly important for quantum computations. The new G-FDTD method is tested by simulation of a particle moving in 2-D free space and then hitting an energy potential. Numerical results coincide with those obtained based on the theoretical analysis.