Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.10860 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- A Schrödinger 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 $V(θ)=2mω_{1}^{2}R^{2}\tan^{2}(θ/2)+2mω_{2}^{2}R^{2}\cot^{2}(θ/2)$, where $0\leqslantθ\leqslantπ$ is the hyperlatitude angular coordinate. In the general case when $ω_{1}\neqω_{2}$, this is a model of a hyperspherical analogue of the Pöschl-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 et al. [Physica E 52 (2013) 122]. For $N\geqslant2$ arbitrary and for $ω_{2}=0$, 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.