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Exact Solutions of the two-dimensional Schrödinger equation with certain central potentials

Shi-Hai Dong
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Abstract

By applying an ansatz to the eigenfunction, an exact closed form solution of the Schrödinger equation in 2D is obtained with the potentials, $V(r)=ar^2+br^4+cr^6$, $V(r)=ar+br^2+cr^{-1}$ and $V(r)=ar^2+br^{-2}+cr^{-4}+dr^{-6}$, respectively. The restrictions on the parameters of the given potential and the angular momentum $m$ are obtained.

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Shi-Hai Dong. 2000-03-22. Exact Solutions of the two-dimensional Schrödinger equation with certain central potentials. https://arxiv.org/abs/quant-ph/0003100

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