原子与分子物理学报, 2005, 22 (3): 443, 网络出版: 2006-06-11
一般Hartmann势Klein-Gordon方程的束缚态
Bound states of Klein-Gordon equation for generalized Hartmann potentials
一般Hartmann势 Klein-Gordon方程 标量势和矢量势 束缚态 Generalized Hartmann potential Klein-Gordon equation Scalar and vector potentials Bound states
摘要
用分离变量方法讨论了在一般Hartmann标量势和矢量势相等条件下Klein-Gordon方程的束缚态解.体系的性质与三个量子数及一般Hartmann势的势参数有关.给出了用广义连带勒让德多项式表示的归一化角向波函数和用合流超几何函数表示的归一化径向波函数,获得了精确的束缚态能谱方程.氢原子势、类氢原子势和Hartmann势是本文一般Hartmann势的三个特例.
Abstract
By using the usual method of variable separation, bound states of Klein-Gord on equation with equal generalized Hartmann scalar and vector potentials are sol ved. Properties of the system relate to three quantum numbers and par ameters of genera lized Hartmann potential. The normalized angle wave function expressed in terms of the universal associated-Legendre polynomial and normalized radial wave func tion expressed in terms of the confluent hypergeometric function are presented. The exact energy spectrum equations are obtained. Hydrogen potential, hydrogen - like potential and Hartmann potential are three special cases for generalized Ha rtmann potential in the Letter.
陆法林, 陈红霞, 陈昌远. 一般Hartmann势Klein-Gordon方程的束缚态[J]. 原子与分子物理学报, 2005, 22(3): 443. 陆法林, 陈红霞, 陈昌远. Bound states of Klein-Gordon equation for generalized Hartmann potentials[J]. Journal of Atomic and Molecular Physics, 2005, 22(3): 443.