An analogue of the Pöschl-Teller anharmonic oscillator on an $N$-dimensional sphere
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929647699099648 |
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| author | Szmytkowski, Radosław |
| author_facet | Szmytkowski, Radosław |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10860 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An analogue of the Pöschl-Teller anharmonic oscillator on an $N$-dimensional sphere Szmytkowski, Radosław Quantum Physics 81Q05 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. |
| title | An analogue of the Pöschl-Teller anharmonic oscillator on an $N$-dimensional sphere |
| topic | Quantum Physics 81Q05 |
| url | https://arxiv.org/abs/2408.10860 |