Bound states of the Schrödinger equation for the Pöschl–Teller double-ring-shaped Coulomb potential

doi:10.1088/1674-1056/19/10/100309

中国物理B ›› 2010, Vol. 19 ›› Issue (10): 100309-100309.doi: 10.1088/1674-1056/19/10/100309

Bound states of the Schrödinger equation for the Pöschl–Teller double-ring-shaped Coulomb potential

陆法林, 陈昌远

School of Physics Science and Electronic Technology, Yancheng Teachers College, Yancheng 224002, China

收稿日期:2009-07-15 修回日期:2010-02-23 出版日期:2010-10-15 发布日期:2010-10-15
基金资助:
Project supported by the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province of China (Grant No. 05KJD140252) and the Natural Science Foundation of Jiangsu Province of China (Grant No. KB2008199).

Bound states of the Schrödinger equation for the Pöschl–Teller double-ring-shaped Coulomb potential

Lu Fa-Lin(陆法林)^† and Chen Chang-Yuan(陈昌远)

School of Physics Science and Electronic Technology, Yancheng Teachers College, Yancheng 224002, China

Received:2009-07-15 Revised:2010-02-23 Online:2010-10-15 Published:2010-10-15
Supported by:
Project supported by the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province of China (Grant No. 05KJD140252) and the Natural Science Foundation of Jiangsu Province of China (Grant No. KB2008199).

摘要/Abstract

摘要： Põschl--Teller double-ring-shaped Coulomb (PTDRSC) potential, the Coulomb potential surrounded by Põschl--Teller and double-ring-shaped inversed square potential, is put forward. In spherical polar coordinates, PTDRSC potential has supersymmetry and shape invariance in φ, θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrõdinger equation with PTDRSC potential are presented. The normalized φ, θ angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of Laguerre polynomials are presented. Energy spectrum equations are obtained. Wave function and energy spectrum equations of the system are related to three quantum numbers and parameters of PTDRSC potential. The solutions of wave functions and corresponding eigenvalues are only suitable for the PTDRSC potential.

Abstract: Põschl–Teller double-ring-shaped Coulomb (PTDRSC) potential, the Coulomb potential surrounded by Pöschl–Teller and double-ring-shaped inversed square potential, is put forward. In spherical polar coordinates, PTDRSC potential has supersymmetry and shape invariance in φ, θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrödinger equation with PTDRSC potential are presented. The normalized φ, θ angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of Laguerre polynomials are presented. Energy spectrum equations are obtained. Wave function and energy spectrum equations of the system are related to three quantum numbers and parameters of PTDRSC potential. The solutions of wave functions and corresponding eigenvalues are only suitable for the PTDRSC potential.

Key words: Pöschl–Teller double-ring-shaped Coulomb potential, supersymmetry and shape invariance, Schrödinger equation, bound states

中图分类号: (Algebraic structures and number theory)

02.10.De

02.10.Ud (Linear algebra) 03.65.Fd (Algebraic methods) 03.65.Ge (Solutions of wave equations: bound states)

陆法林, 陈昌远. Bound states of the Schrödinger equation for the Pöschl–Teller double-ring-shaped Coulomb potential[J]. 中国物理B, 2010, 19(10): 100309-100309.

Lu Fa-Lin(陆法林) and Chen Chang-Yuan(陈昌远). Bound states of the Schrödinger equation for the Pöschl–Teller double-ring-shaped Coulomb potential[J]. Chin. Phys. B, 2010, 19(10): 100309-100309.

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Bound states of the Schrödinger equation for the Pöschl–Teller double-ring-shaped Coulomb potential

Bound states of the Schrödinger equation for the Pöschl–Teller double-ring-shaped Coulomb potential

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