Analytical Solutions of the Manning-Rosen Potential In the Tridiagonal Program
ZHANG Min-Cang1**, AN Bo2
1College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062 2Department of Physics and Electronic Engineering, Weinan Teachers University, Weinan 714000
Analytical Solutions of the Manning-Rosen Potential In the Tridiagonal Program
ZHANG Min-Cang1**, AN Bo2
1College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062 2Department of Physics and Electronic Engineering, Weinan Teachers University, Weinan 714000
摘要The Schrödinger equation with the Manning-Rosen 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 Schrödinger equation is translated into finding solutions of the resulting three-term recursion relation for the expansion coefficients of the wavefunction. The discrete spectrum of the bound states is obtained by diagonalization of the recursion relation with special choice of the parameters and the wavefunctions is expressed in terms of the Jocobi polynomial.
Abstract：The Schrödinger equation with the Manning-Rosen 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 Schrödinger equation is translated into finding solutions of the resulting three-term recursion relation for the expansion coefficients of the wavefunction. The discrete spectrum of the bound states is obtained by diagonalization of the recursion relation with special choice of the parameters and the wavefunctions is expressed in terms of the Jocobi polynomial.
ZHANG Min-Cang**;AN Bo
. Analytical Solutions of the Manning-Rosen Potential In the Tridiagonal Program[J]. 中国物理快报, 2010, 27(11): 110301-110301.
ZHANG Min-Cang**, AN Bo
. Analytical Solutions of the Manning-Rosen Potential In the Tridiagonal Program. Chin. Phys. Lett., 2010, 27(11): 110301-110301.
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