中国物理B ›› 2007, Vol. 16 ›› Issue (7): 1863-1867.doi: 10.1088/1009-1963/16/7/010

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Exact solutions of the Klein--Gordon equation with Makarov potential and a recurrence relation

张民仓, 王振邦   

  1. School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
  • 收稿日期:2006-10-31 修回日期:2006-11-27 出版日期:2007-07-20 发布日期:2007-07-04

Exact solutions of the Klein--Gordon equation with Makarov potential and a recurrence relation

Zhang Min-Cang(张民仓)† and Wang Zhen-Bang(王振邦)   

  1. School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
  • Received:2006-10-31 Revised:2006-11-27 Online:2007-07-20 Published:2007-07-04

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摘要： In this paper, the Klein--Gordon equation with equal scalar and vector Makarov potentials is studied by the factorization method. The energy equation and the normalized bound state solutions are obtained, a recurrence relation between the different principal quantum number n corresponding to a certain angular quantum number \ell is established and some special cases of Makarov potential are discussed.

关键词: Makarov potential, Klein--Gordon equation, bound state, factorization method

Abstract: In this paper, the Klein--Gordon equation with equal scalar and vector Makarov potentials is studied by the factorization method. The energy equation and the normalized bound state solutions are obtained, a recurrence relation between the different principal quantum number n corresponding to a certain angular quantum number $\ell$ is established and some special cases of Makarov potential are discussed.

Key words: Makarov potential, Klein--Gordon equation, bound state, factorization method

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

  • 03.65.Ge
02.10.Ud (Linear algebra) 03.65.Fd (Algebraic methods)