Moxley III, Frederick Ira and Zhu, Fei and Dai, Weizhong (2012) A Generalized FDTD Method with Absorbing Boundary Condition for Solving a Time-Dependent Linear Schrodinger Equation. American Journal of Computational Mathematics, 02 (03). pp. 163-172. ISSN 2161-1203
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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 iterative process. However, the method provides only a second-order accurate numerical solution and requires that the spatial grid size and time step should satisfy a very restricted condition in order to prevent the numerical solution from diverging. In this article, we present a generalized FDTD method with absorbing boundary condition for solving the one-dimensional (1D) time-dependent Schr?dinger equation and obtain a more relaxed condition for stability. The generalized FDTD scheme is tested by simulating a particle moving in free space and then hitting an energy potential. Numerical results coincide with those obtained based on the theoretical analysis.
Item Type: | Article |
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Subjects: | STM One > Mathematical Science |
Depositing User: | Unnamed user with email support@stmone.org |
Date Deposited: | 19 Jun 2023 07:20 |
Last Modified: | 16 Sep 2024 10:14 |
URI: | http://publications.openuniversitystm.com/id/eprint/1427 |