<em>L</em><sup>2</sup>基的组态空间中修正Poschl-Teller势的精确解

陈发堂1，张民仓2

doi:10.3969/j.issn.1007-2861.2011.05.009

上海大学学报(自然科学版) >

2011 , Vol. 17 >Issue 5: 620 - 623

DOI: https://doi.org/10.3969/j.issn.1007-2861.2011.05.009

数理化科学

L²基的组态空间中修正Poschl-Teller势的精确解

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1.上海电力学院数学物理系,上海 200090; 2.陕西师范大学物理学与信息技术学院,西安 710062

收稿日期: 2011-03-04

网络出版日期: 2011-10-26

基金资助

国家教育部重点实验室资助项目（P201006）；上海市教委科研创新基金资助项目（11ZZ172）；上海市教委重点学科建设资助项目（G51304）；上海市自然科学基金资助项目（09ZR1413000）

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Exact Solutions of Modified Poschl-Teller Potential in Configuration Space of L²Basis

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1. Department of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China; 2. College of Physics and Information Technology, Shaanxi Normal University, Xi’an 710062, China

Received date: 2011-03-04

Online published: 2011-10-26

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摘要

在完全平方可积的L²空间中求解修正Poschl-Teller势满足的Schrodinger方程.由于L²空间能够负载波算子的三对角化矩阵表示，因而求解修正Poschl-Teller势满足的Schrodinger方程转变为寻求波函数展开系数满足的一个三项递推关系式.研究结果表明，相应的束缚态波函数可以由Jacobi多项式表示，束缚态的能谱方程可以由波函数展开系数递推关系式的对角化条件得到.

关键词： 平方可积空间; 三对角化矩阵方案; 修正Poschl-Teller势; 正交多项式

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陈发堂1，张民仓2 . L²基的组态空间中修正Poschl-Teller势的精确解[J]. 上海大学学报(自然科学版), 2011 , 17(5) : 620 -623 . DOI: 10.3969/j.issn.1007-2861.2011.05.009

Abstract

The Schrodinger equation with the modified Poschl-Teller potential is studied by working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator. In this program, solving the Schrodinger equation is translated into finding solutions of a resulting three-term recursion relation for expansion coefficients of the wave functions. It is shown that with the tridiagonal representation, the wave function of the Schrodinger equation is expressed in terms of the Jacobi polynomial and the discrete spectrum of the bound states is obtained by diagonalization of the recursion relation.

Key words： modified Poschl-Teller potential; orthogonal polynomials; square integrable basis; tridiagonal matrix program

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