新环状非球谐振子势的Dirac方程束缚态解  

The bound states solution of dirac equation for a new ring-shaped non-spherical harmonic oscillator potentials

作　　者：胡先权[1] 王帮美[1] 崔立鹏[1] 

机构地区：[1]重庆师范大学物理学与信息技术学院,重庆400047

出　　处：《原子与分子物理学报》2009年第3期429-434,共6页Journal of Atomic and Molecular Physics

基　　金：国家自然科学基金(10575140);重庆市教委基础理论研究基金(KJ080825)

摘　　要：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Dirac方程的束缚态解.通过分离变量得到Dirac方程相应的角向方程和径向方程,得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并对结果作适当讨论与结论.A new ring-shaped non-harmonic oscillator potential is proposed. The exact bound solution of Dirac equation for the above potential is obtained under the condition of equal scalar and vector potentials. Dirac equation can be separated into an angular equation and a radial equation with the help of separation variable. The normalized angle wave function expressed and radial wave function expressed respectively in terms of the universal associated-Legendre function and the confluent hypergeometric function are presented. The exact energy spectrum equations are obtained and meanwhile, proper discussion and some important conclusions are presented.

关 键 词：环状非球谐振子势 DIRAC方程 束缚态 广义连带勒让德多项式 

分 类 号：O562.1[理学—原子与分子物理] O413.1[理学—物理]