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

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