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

页码：120 / 132

页数：13

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