Analytical Approximation to the ℓ-Wave Solutions of the Hulthén Potential in Tridiagonal Representation
ZHANG Min-Cang1**, HUANG-FU Guo-Qing 2
1College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062 2Department of Physics and Electronic Engineering, Weinan Teachers University, Weinan 714000
Analytical Approximation to the ℓ-Wave Solutions of the Hulthén Potential in Tridiagonal Representation
ZHANG Min-Cang1**, HUANG-FU Guo-Qing 2
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 Hulthén potential is studied by working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator. The arbitrary ℓ-wave solutions are obtained by using an approximation of the centrifugal term. The resulting three-term recursion relation for the expansion coefficients of the wavefunction is presented and the wavefunctions are expressed in terms of the Jacobi polynomial. The discrete spectrum of the bound states is obtained by the diagonalization of the recursion relation.
Abstract:The Schrödinger equation with the Hulthén potential is studied by working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator. The arbitrary ℓ-wave solutions are obtained by using an approximation of the centrifugal term. The resulting three-term recursion relation for the expansion coefficients of the wavefunction is presented and the wavefunctions are expressed in terms of the Jacobi polynomial. The discrete spectrum of the bound states is obtained by the diagonalization of the recursion relation.
ZHANG Min-Cang**;HUANG-FU Guo-Qing
. Analytical Approximation to the ℓ-Wave Solutions of the Hulthén Potential in Tridiagonal Representation[J]. 中国物理快报, 2011, 28(5): 50304-050304.
ZHANG Min-Cang**, HUANG-FU Guo-Qing
. Analytical Approximation to the ℓ-Wave Solutions of the Hulthén Potential in Tridiagonal Representation. Chin. Phys. Lett., 2011, 28(5): 50304-050304.
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