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

2024/08/20 by Radosław Szmytkowski, Szmytkowski, Radosław
Computer Science · Mathematics · #81Q05 #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Numerical methods in inverse problems #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2408.10860

openalex publication_date 2024/08/20 · openalex created_date 2024/10/01 · openalex updated_date 2026/07/28

Abstract

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)=2mω₁²R²tan²(θ/2)+2mω₂²R²\cot²(θ/2), where 0\leqslantθ\leqslantπ is the hyperlatitude angular coordinate. In the general case when ω₁≠ω₂, 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 ω₂=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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