双环形Hulth ´en势束缚态的近似解析解

摘要

The double ring-shaped Hulth ´en potential is proposed in this paper. By using the analytical method of function, the approximate analytical solutions of bound state solutions of Schr ¨odinger equation for the double ring-shaped Hulth ´en potential are presented within the framework of an exponential approximation of the centrifugal potential for arbitrary l-states. The normalized angular and radial wave function expressed in terms of hypergeometric polynomials are presented. The energy spectrum equations are obtained. The wave function and the energy spectrum equations of the system are related to three quantum numbers and parameters of double ring-shaped Hulth´en potential. The polar angular wave functions of the central potential and ring-shaped potential and the energy spectrum equations of Hulth ´en potential turn out to be the special cases of the double ring-shaped Hulth ´en potential.%构造了双环形Hulth´en势，用指数函数近似表示任意分波的离心项，运用函数分析法讨论双环型Hulth´en势Schr ¨odinger方程的束缚态解。归一化的角向波函数和径向波函数用超几何多项式表示，给出了束缚态能谱，体系的束缚态的能谱方程和波函数与量子数和势参数有关。中心势场和单环形势场角向波函数及Hulth´en势束缚态能谱是本文双环形Hulth´en势的特例。