Schrödinger Equation with the Potential $V(r)=a r^2+b r^{-4}+c r^{-6}$

Dong, Shi-Hai; Hou, Xi-wen; Ma, Zhong-Qi

Schrödinger Equation with the Potential $V(r)=a r^2+b r^{-4}+c r^{-6}$

Authors

Dong, Shi-Hai

Hou, Xi-wen

Ma, Zhong-Qi

Description

By making use of an ${\it ansatz}$ for the eigenfunction, we obtain the exact solutions to the Schrödinger equation with the anharmonic potential, $V(r)=a r^2+b r^{-4}+c r^{-6}$, both in three dimensions and in two dimensions, where the parameters $a$, $b$, and $c$ in the potential satisfy some constraints.
PS file 10 pages, Submitted to J.P.A