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

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

2000-03-22

arxiv.org/abs/quant-ph/0003100v1

Physics

Quantum Physics

Latex files and accepted by Inter. J. Theor. Phys. 39, No. 4

Scientific paper

By applying an ansatz to the eigenfunction, an exact closed form solution of
the Schr\"{o}dinger 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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