Solving the time-dependent Schrodinger equation using finite difference methods

被引：0
|
作者：
Becerril, R. [1 ]
Guzman, F. S. [1 ]
Rendon-Romero, A. [2 ]
Valdez-Alvarado, S. [1 ]
机构：
[1] Univ Michoacana, Inst Fis & Matemat, Morelia 58040, Michoacan, Mexico
[2] Univ Michoacana, Fac Ciencias Fisicomatemat, Morelia 58040, Michoacan, Mexico
来源：
REVISTA MEXICANA DE FISICA E | 2008年 / 54卷 / 02期
关键词：
Finite difference methods; computational techniques; Schroedinger equation;
D O I：
暂无
中图分类号：
N09 [自然科学史]; B [哲学、宗教];
学科分类号：
01 ; 0101 ; 010108 ; 060207 ; 060305 ; 0712 ;
摘要：
We solve the time-dependent Schrodinger equation in one and two dimensions using the finite difference approximation. The evolution is carried out using the method of lines. The illustrative cases include: the particle in a box and the harmonic oscillator in one and two dimensions. As non-standard examples we evolve two solitons and show the time-dependent solitonic behavior in one dimension and the stabilization of an atomic gas model in two dimensions. The codes used to generate the results in this manuscript are freely available under request, and we expect this material could help students to have a better grasp of the solution of partial differential equations related to dynamical systems.
引用
收藏
页码：120 / 132
页数：13
相关论文
共 50 条
  • [31] Superconvergence analysis of finite element method for the time-dependent Schrodinger equation
    Wang, Jianyun
    Huang, Yunqing
    Tian, Zhikun
    Zhou, Jie
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 71 (10) : 1960 - 1972
  • [32] Exact boundary conditions at finite distance for the time-dependent Schrodinger equation
    Mangin-Brinet, M
    Carbonell, J
    Gignoux, C
    PHYSICAL REVIEW A, 1998, 57 (05): : 3245 - 3255
  • [33] On finite difference methods for the solution of the Schrodinger equation
    Simos, TE
    Williams, PS
    COMPUTERS & CHEMISTRY, 1999, 23 (06): : 513 - 554
  • [34] Exact boundary conditions at finite distance for the time-dependent Schrodinger equation
    Mangin-Brinet, M.
    Carbonell, J.
    Gignoux, C.
    Physical Review A. Atomic, Molecular, and Optical Physics, 1998, 57 (05):
  • [35] A TIME-DEPENDENT SCHRODINGER-EQUATION
    KRANOLD, HU
    JOURNAL OF MATHEMATICAL PHYSICS, 1983, 24 (09) : 2345 - 2347
  • [36] On the derivation of the time-dependent equation of Schrodinger
    Briggs, JS
    Rost, JM
    FOUNDATIONS OF PHYSICS, 2001, 31 (04) : 693 - 712
  • [37] On the time-dependent solutions of the Schrodinger equation
    Palma, Alejandro
    Pedraza, I.
    TOPICS IN THE THEORY OF CHEMICAL AND PHYSICAL SYSTEMS, 2007, 16 : 147 - +
  • [38] Analysis of Finite Difference Time Domain Technique to Solve the Time-dependent Schrodinger Equation in Quantum Structures in Inhomogeneous Medium
    Guo, Wenting
    Lan, Jin
    Wang, Xiaoying
    Peng, Yangyang
    Sui, Wenquan
    INEC: 2010 3RD INTERNATIONAL NANOELECTRONICS CONFERENCE, VOLS 1 AND 2, 2010, : 171 - +
  • [39] Symplectic Pseudospectral Time-Domain Scheme for Solving Time-Dependent Schrodinger Equation
    Shen, Jing
    Sha, Wei E. I.
    Kuang, Xiaojing
    Hu, Jinhua
    Huang, Zhixiang
    Wu, Xianliang
    PROGRESS IN ELECTROMAGNETICS RESEARCH M, 2018, 66 : 109 - 118
  • [40] Solving the Schrodinger equation for a charged particle in a magnetic field using the finite difference time domain method
    Sudiarta, I. Wayan
    Geldart, D. J. Wallace
    PHYSICS LETTERS A, 2008, 372 (18) : 3145 - 3148
12345