一类环状非球谐振子势场中相对论粒子的束缚态解

提出了一种新的环状非球谐振子势, 在标量势与矢量势相等的条件下，给出了其Klein-Gordon方程和Dirac方程的束缚态解. Klein-Gordon方程的θ角向波函数以超几何函数表示，径向波函数可用合流超几何函数或广义拉盖尔多项式表示，能谱方程由径向波函数满足的束缚态边界条件得到. Dirac方程的旋量波函数可用Klein-Gordon方程的解构造. 关键词： 环状非球谐振子势 Klein-Gordon方程 Dirac方程 束缚态

Bound state solutions of relativistic particles in a new ring-shaped non-harmonic oscillator potential

In this paper, a new ring-shaped non-harmonic oscillator potential is proposed. Under the condition of equal scalar and vector potentials, the exact bound solutions and energy equations of both the Klein-Gordon equation and Dirac equation for this oscillator potential are obtained. It is shown that the angular wave functions of Klein-Gordon equation are given by the hypergeometric functions and the radial wave functions are expressed in terms of the confluent hypergeometric functions or general Laguerre polynomial. The spinner wave functions of the Dirac equation are constructed with the of the Klein-Gordon equation.