中国物理B ›› 2005, Vol. 14 ›› Issue (3): 463-467.doi: 10.1088/1009-1963/14/3/005

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Bound states of Klein—Gordon equation for double ring-shaped oscillator scalar and vector potentials

陆法林, 陈昌远, 孙东升   

  1. Department of Physics, Yancheng Teachers' College, Yancheng 224002, China
  • 收稿日期:2004-05-20 修回日期:2004-10-06 出版日期:2005-03-02 发布日期:2005-03-02
  • 基金资助:
    Project supported by the Natural Science Foundation of the Education Bureau of Jiangsu Province, China (Grant No 02KJB140007), and the Special Foundation of Yancheng Teachers College, China.

Bound states of Klein—Gordon equation for double ring-shaped oscillator scalar and vector potentials

Lu Fa-Lin (陆法林), Chen Chang-Yuan (陈昌远), Sun Dong-Sheng (孙东升)   

  1. Department of Physics, Yancheng Teachers' College, Yancheng 224002, China
  • Received:2004-05-20 Revised:2004-10-06 Online:2005-03-02 Published:2005-03-02
  • Supported by:
    Project supported by the Natural Science Foundation of the Education Bureau of Jiangsu Province, China (Grant No 02KJB140007), and the Special Foundation of Yancheng Teachers College, China.

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摘要： In spherical polar coordinates, double ring-shaped oscillator potentials have supersymmetry and shape invariance for θ and r coordinates. Exact bound state solutions of Klein—Gordon equation with equal double ring-shaped oscillator scalar and vector potentials are obtained. The normalized angular wavefunction expressed in terms of Jacobi polynomials and the normalized radial wavefunction expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.

关键词: double ring-shaped oscillator potentials, supersymmetry and shape invariance, Klein—Gordon equation, scalar and vector potentials, bound states

Abstract: In spherical polar coordinates, double ring-shaped oscillator potentials have supersymmetry and shape invariance for $\theta$ and r coordinates. Exact bound state solutions of Klein—Gordon equation with equal double ring-shaped oscillator scalar and vector potentials are obtained. The normalized angular wavefunction expressed in terms of Jacobi polynomials and the normalized radial wavefunction expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.

Key words: double ring-shaped oscillator potentials, supersymmetry and shape invariance, Klein—Gordon equation, scalar and vector potentials, bound states

中图分类号:  (Solutions of wave equations: bound states)

  • 03.65.Ge
02.10.De (Algebraic structures and number theory)