An analogue of the Pöschl–Teller anharmonic oscillator on an N-dimensional sphere

Radosław Szmytkowski

doi:10.1140/epjp/s13360-025-06252-w

An analogue of the Pöschl–Teller anharmonic oscillator on an N-dimensional sphere

Abstract

A Schr{\"o}dinger particle on an $N$-dimensional ($N\geqslant2$) hypersphere of radius $R$ is considered. The particle is subjected to the action of a force characterized by the potential $V(\theta)=2m\omega_{1}^{2}R^{2}\tan^{2}(\theta/2) +2m\omega_{2}^{2}R^{2}\cot^{2}(\theta/2)$, where $0\leqslant\theta\leqslant\pi$ is the hyperlatitude angular coordinate. In the general case when $\omega_{1}\neq\omega_{2}$, this is a model of a hyperspherical analogue of the P{\"o}schl--Teller anharmonic oscillator. Energy eigenvalues and normalized eigenfunctions for this system are found in closed analytical forms. For $N=2$, our results reproduce those obtained by Kazaryan \emph{et al.\/} [Physica E 52 (2013) 122]. For $N\geqslant2$ arbitrary and for $\omega_{2}=0$, the results of Mardoyan and Petrosyan [J.Contemp. Phys. 48 (2013) 70}] for their model of an isotropic hyperspherical harmonic oscillator are recovered. The Euclidean limit for the anharmonic oscillator in question is also discussed.

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Radosław Szmytkowski prof. dr hab.

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Articles

Type:

artykuły w czasopismach

Published in:

European Physical Journal Plus no. 140,
ISSN: 2190-5444

Language:

English

Publication year:

2025

Bibliographic description:

Szmytkowski R.: An analogue of the Pöschl–Teller anharmonic oscillator on an N-dimensional sphere// European Physical Journal Plus -Vol. 140,iss. 5 (2025), s.361/1-361/11

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