一类新的环状非有心谐振子势的精确解  

Exact solutions of the Schrdinger equation for a new ring-shaped noncentral potential

作　　者：陈发堂[1] 张民仓[2] 

机构地区：[1]上海电力学院数理系,上海200090 [2]陕西师范大学物理学与信息技术学院,陕西西安710062

出　　处：《陕西师范大学学报（自然科学版）》2011年第4期29-33,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：上海市自然科学基金资助项目(09ZR1413000);上海市教委科研创新基金资助项目(11ZZ172)

摘　　要：提出了一个新的环状非有心谐振子势模型.利用Nikiforov-Uvarov(N-U)方法,求解了其满足的Schr dinger方程,得到了其束缚态波函数的精确解及能谱方程.结果表明:束缚态的角向波函数可以用广义超球多项式或超几何函数表示,径向波函数则可以连带Laguerre多项式表示.讨论了这一势模型中角向分量对径向分量的影响,指出当相关的参数取特定值时,新的环状非有心谐振子势可退化为不同的模型.A new ring-shaped noncentral potential is proposed.The exactly complete solutions of the Schrdinger equation with this model potential are presented by the Nikiforov-Uvarov（N-U）method.It is shown that the component of bound state wavefunction could be expressed by the generalized ultraspherical polynomial or the hypergeometric function,and the radial component is given in terms of the associated Laguerre polynomial.Finally,the effect of the angle-dependent part on the radial solutions and several particular cases of this potential are also dicussed.

关 键 词：环状非有心势 Schrdinger方程 束缚态 Nikiforov-Uvarov方法 

分 类 号：O413.1[理学—理论物理]