高次正幂与逆幂势函数叠加的径向薛定谔方程的求解研究  

A Study of the Solution of the Radial Schrdinger Equation in the Superposition Potential with the High Order Power and Inverse-power Potential Function

作　　者：胡先权[1] 欧红叶[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：《重庆师范大学学报（自然科学版）》2007年第3期36-37,共2页Journal of Chongqing Normal University:Natural Science

基　　金：重庆市科委自然科学基金项目(No.2005BB8267);重庆教委基础理论研究基金项目(No.KJ060813)

摘　　要：When Schr dinger equation appears with high order power and inverse power potential function or the superposed potential function which is the high order anharmonic oscillator potential.the electric dipole moment potential,the molecular crystal potential.The polarized equivalent potential,the solution process of the Schr dinger equation is very complex.In recent years,many researchers have devoted their attention to the analytic solution of the Schr dinger equation that includes high power and inverse power potential function.Their achievements play an important role in improving the quantum theory.For the special potential function which are linearly superposed by high power and inverse power potential function.One of the analytic solutions has been found such as the potential function V(r)=ar2+br-4+cr-6 in references [7],the unharmonic oscillator potential function V(x)=x2/2+g/(2x2) in references ,and the potential function of the molecular crystal V(r)=A1r-10-A2r-6 in references ,yet those functions are usually necessary to limit the coefficient of the power term and have internal relations for those exact solution.In this paper,the combination of series solution and asymptotic solution are utilized near singular points,a series analytic solution of the wave functions of stationary state for radial Schr dinger equation with potential function V(r)=a1r6+a2r2+a3r-4+a4r-6and the corresponding energy level structure are obtained under the tightly-coupled condition of the interactional power potential functions.Meanwhile,the paper puts forward proper discussions and draws some important conclusions.When Schr dinger equation appears with high order power and inverse power potential function or the superposed potential function which is the high order anharmonic oscillator potential, the electric dipole moment potential, the molecular crystal potential. The polarized equivalent potential , the solution process of the Schr dinger equation is very complex. In recent years, many researchers have devoted their attention to the analytic solution of the Schr dinger equation that includes high power and inverse power potential function. Their achievements play an important role in improving the quantum theory. For the special potential function which are linearly superposed by high power and inverse power potential function. One of the analytic solutions has been found such as the potential function V（ r ） = ar^2 ＋ br^-4 ＋ cr^-6 in references [7], the unharmonic oscillator potential function V（ x ） =x^2/2 ＋ g/ （ 2x62） in references [ 13 ], and the potential function of the molecular crystal V（r） = A1r^-10 -A2r^-6 in references [ 15 ], yet those functions are usually necessary to limit the coefficient of the power term and have internal relations for those exact solution. In this paper, the combination of series solution and asymptotic solution are utilized near singular points, a series analytic solution of the wave functions of stationary state for radial Schr dinger equation with potential function V（r） = a1 r^6 ＋ a2r^2 ＋ a3r^-4 ＋ a4r^-6and the corresponding energy level struc- ture are obtained under the tightly - coupled condition of the interactional power potential functions. Meanwhile, the paper puts forward proper discussions and draws some important conclusions.

关 键 词：幂势函数 径向波函数 渐近解 解析解 

分 类 号：O562[理学—原子与分子物理] O413[理学—物理]