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

在一般参考文献中,对于薛定谔方程解析解的研究,只讨论了势函数为库仑势或谐振子势时的本征波函数及其本征值(能级)的严格求解,对于复杂的原子体系,其能量状态由组成原子的各个粒子之间的相互作用力决定。各个电子除受到原子核的中心库仑力作用外,各个电子之间还存在非中心静电

A Study of the Solution of the Radial Schr(o)dinger Equation in the Superposition Potential with the High Order Power and Inverse-power Potential Function

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.