用基函数展开法求解一维有限深方势阱模型

大学物理 ›› 2016, Vol. 35 ›› Issue (8): 39-43.

用基函数展开法求解一维有限深方势阱模型

王再军

天津职业技术师范大学理学院，天津300222

收稿日期:2015-07-07 修回日期:2016-01-22 出版日期:2016-08-20 发布日期:2016-08-20
作者简介:王再军( 1964—) ，男，河南濮阳人，天津职业技术师范大学教授，主要从事理论核物理和量子物理的研
基金资助:
国家自然科学基金( 11275138) 、天津职业技术师范大学科研基金( KJYB11-3) 资助

Solution of one-dimensional finite symmetric square potential well model using the basis expansion method

WANG Zai-jun

School of Science，Tianjin University of Technology and Education，Tianjin 300222，China

Received:2015-07-07 Revised:2016-01-22 Online:2016-08-20 Published:2016-08-20

摘要/Abstract

摘要： 用基函数展开法求解了一维有限深方势阱模型，所得结果与在坐标表象中直接求解薛定谔方程所得结果完全一致.重要的是这一求解过程为量子力学中基函数展开方法的教授与学习提供了一个范例，也为量子力学问题的计算机求解的教与学提供了参考.

关键词: 一维有限深方势阱模型, 基函数展开法, 谐振子本征函数, 算符的矩阵表示

Abstract: The one - dimensional finite symmetric square potential well model is studied by using the basis expansion method. The results are in agreement well with those obtained ones by solving the Schrdinger equation in the coordinate representation. The calculation is a good illustration of the basis expansion method in the quantum mechanics and provides a good example for teaching and studying of the method. In addition，numerical evaluation of the results also provides a good reference for teaching and studying of solving quantum problems by using computers.

Key words: one-dimensional finite symmetric square potential well model, basis expansion method, harmonic oscillator eigenfunction, matrix representation of operator

王再军. 用基函数展开法求解一维有限深方势阱模型[J]. 大学物理, 2016, 35(8): 39-43.

WANG Zai-jun. Solution of one-dimensional finite symmetric square potential well model using the basis expansion method[J]. College Physics, 2016, 35(8): 39-43.