一般Hartmann势Klein-Gordon方程的束缚态

Bound states of Klein-Gordon equation for generalized Hartmann potentials

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。

By using the usual method of variable separation, bound states of Klein-Gordon equation with equal generalized Hartmann scalar and vector potentials are solved. Properties of the system relate to three quantum numbers and parameters of generalized Hartmann potential. The normalized angle wave function expressed in terms of the universal associated-Legendre polynomial and normalized radial wave function 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 eases for generalized Hartmann potential in the Letter.