# On the harmonic oscillator on the Lobachevsky plane - Mathematical Physics

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Abstract: We introduce the harmonic oscillator on the Lobachevsky plane with the aid ofthe potential $Vr=a^2\omega^2-4sinhr-a^2$ where $a$ is the curvatureradius and $r$ is the geodesic distance from a fixed center. Thus the potentialis rotationally symmetric and unbounded likewise as in the Euclidean case. Theeigenvalue equation leads to the differential equation of spheroidal functions.We provide a basic numerical analysis of eigenvalues and eigenfunctions in thecase when the value of the angular momentum, $m$, equals 0.

Autor: P. Stovicek, M. Tusek

Fuente: https://arxiv.org/