Exact Solutions to the Schrödinger Equation for the potential $V(r)=a r^2+b r^{-4}+c r^{-6}$ in 2D

Shi-Hai Dong, Zhong-Qi Ma

备注：: Latex file, pages 9 and 2 eps figures, accepted by J. Phys. A
DOI：: 10.1088/0305-4470/31/49/009

英文摘要：

Making use of an ${\it ansatz}$ for the eigenfunctions, we obtain an exact closed form solution to the non-relativistic Schrödinger equation with the anharmonic potential, $V(r)=a r^2+b r^{-4}+c r^{-6}$ in two dimensions, where the parameters of the potential $a, b, c$ satisfy some constraints.

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