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 pote...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.展开更多
文摘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.
