Simulation of Time-Dependent Schrödinger Equation in the Position and Momentum Domains

• 作者: Michael Jennings
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: Schr?dinger Equation PREDICTOR-CORRECTOR FOURIER Transform MOMENTUM Domain
• 年，卷（期）: 2015,（3）
• 页码范围: 291-303
• 页数: 13页
• 分类号: O1

摘要

The paper outlines the development of a new, spectral method of simulating the Schrödinger equation in the momentum domain. The kinetic energy operator is approximated in the momentum domain by exploiting the derivative property of the Fourier transform. These results are compared to a position-domain simulation generated by a fourth-order, centered-space, finite-difference formula. The time derivative is approximated by a four-step predictor-corrector in both domains. Free-particle and square-well simulations of the time-dependent Schrödinger equation are run in both domains to demonstrate agreement between the new, spectral methods and established, finite-difference methods. The spectral methods are shown to be accurate and precise.