Solving the time-dependent Schrödinger equation using finite difference methods

Authors

  • R. Becerril
  • F.S. Guzmán
  • A. Rendón-Romero
  • S. Valdez-Alvarado

Keywords:

Finite difference methods, computational techniques, Schröedinger equation

Abstract

We solve the time-dependent Schrödinger 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.

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Published

2008-01-01

How to Cite

[1]
R. Becerril, F. Guzmán, A. Rendón-Romero, and S. Valdez-Alvarado, “Solving the time-dependent Schrödinger equation using finite difference methods”, Rev. Mex. Fis. E, vol. 54, no. 2 Jul-Dec, pp. 120–132, Jan. 2008.

Issue

Vol. 54 No. 2 Jul-Dec (2008): Revista Mexicana de Física E

Section

Artículos

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