L^2基的组态空间中修正Pschl-Teller势的精确解  

Exact Solutions of Modified Pschl-Teller Potential in Configuration Space of L^2 Basis

作　　者：陈发堂[1] 张民仓[2] 

机构地区：[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

出　　处：《上海大学学报（自然科学版）》2011年第5期620-623,共4页Journal of Shanghai University:Natural Science Edition

基　　金：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)

摘　　要：在完全平方可积的L2空间中求解修正Pschl-Teller势满足的Schrdinger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Pschl-Teller势满足的Schrdinger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.The Schrdinger equation with the modified Pschl-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 Schrdinger 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 Schrdinger 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.

关 键 词：修正Pschl-Teller势 三对角化矩阵方案 平方可积空间 正交多项式 

分 类 号：O413.1[理学—理论物理]