Exact Solutions to the Schrödinger Equation for the potential $V(r)=a r^2+b r^{-4}+c r^{-6}$ in 2D

Details Exact Solutions to the Schrödinger Equation for the potential $V(r)=a r^2+b r^{-4}+c r^{-6}$ in 2D Exact Solutions to the Schrödinger Equation for the potential $V(r)=a r^2+b r^{-4}+c r^{-6}$ in 2D

1998-10-19

arxiv.org/abs/quant-ph/9810056v1

Physics

Quantum Physics

Latex file, pages 9 and 2 eps figures, accepted by J. Phys. A

Scientific paper

10.1088/0305-4470/31/49/009

Making use of an ${\it ansatz}$ for the eigenfunctions, we obtain an exact
closed form solution to the non-relativistic Schr\"{o}dinger 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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