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Exact Solutions to the Schrödinger Equation for the Inverse-Power Potential in Two Dimensions

Shi-Hai Dong·Zhong-Qi Ma
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Abstract

Utilizing an ${\it ansatz}$ for the eigenfunctions, we arrive at an exact closed form solution to the Schrödinger equation with the inverse-power potential, $V(r)=ar^{-4}+br^{-3}+cr^{-2}+dr^{-1}$ in two dimensions, where the parameters of the potential $a, b, c, d$ satisfy a constraint.

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Shi-Hai Dong, Zhong-Qi Ma. 1999-01-15. Exact Solutions to the Schrödinger Equation for the Inverse-Power Potential in Two Dimensions. https://arxiv.org/abs/quant-ph/9901036

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