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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
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Abstract

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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Shi-Hai Dong, Zhong-Qi Ma. 1998-10-19. Exact Solutions to the Schrödinger Equation for the potential $V(r)=a r^2+b r^{-4}+c r^{-6}$ in 2D. https://doi.org/10.1088/0305-4470%2F31%2F49%2F009

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