高次正幂与逆幂势函数的叠加的径向薛定谔方程的解析解  

The analytic solution of the radial Schrdinger equation for the superposed potential of high-order power and inverse-power potential functions

作　　者：胡先权[1] 许杰[1] 马勇[1] 殷霖[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：《物理学报》2007年第9期5060-5065,共6页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10147207);重庆市科委自然科学基金(批准号:2005BB8267);重庆市教委基础理论研究基金(批准号:KJ060813)资助的课题.~~

摘　　要：当薛定谔方程中出现高次非谐振子势,电偶极矩势,分子晶体势,极化等效势等高次正幂与逆幂势函数以及它们的叠加时,薛定谔方程的求解变得非常复杂,采用奇点邻域附近的级数解法与求解渐近解相结合,在多种相互作用幂函数紧密耦合的条件下,得到势函数为V(r)=a1r6+a2r2+a3r-4+a4r-6的径向薛定谔方程的一系列定态波函数解析解以及能级结构.When the Schrdinger equation involves high-order power and inverse power potential functions or the superposed potential function of high-order anharmonic oscillatory potentials, introduced by the presence of electric dipole moment potential, molecular crystal potential, or the polarized equivalent potential, the solution of the Schrdinger equation becomes very complicated. In this paper, with the help of a combination of series solutions and asymptotic solutions utilized near the singular points, a series analytic solution of the wave functions of stationary state for radial Schrdinger equation with potential function V（r） =a1r^6＋a2r^2＋a3r^-4 ＋a4r^-6 and the corresponding energy level structure are obtained under the tightly-coupled condition of the interacting power potential functions. Meanwhile, the paper gives a proper discussion and some important conclusions are drawn.

关 键 词：级数解法 幂势函数 径向波函数 渐近解 

分 类 号：O411.1[理学—理论物理] O175.24[理学—物理]