Schrödinger Equation with the Potential $V(r)=a r^2+b r^{-4}+c r^{-6}$

Details Schrödinger Equation with the Potential $V(r)=a r^2+b r^{-4}+c r^{-6}$ Schrödinger Equation with the Potential $V(r)=a r^2+b r^{-4}+c r^{-6}$

1998-08-21

arxiv.org/abs/quant-ph/9808037v1

Physics

Quantum Physics

PS file 10 pages, Submitted to J.P.A

Scientific paper

By making use of an ${\it ansatz}$ for the eigenfunction, we obtain the exact
solutions to the Schr\"{o}dinger equation with the anharmonic potential,
$V(r)=a r^2+b r^{-4}+c r^{-6}$, both in three dimensions and in two dimensions,
where the parameters $a$, $b$, and $c$ in the potential satisfy some
constraints.

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