Year: 2025
Type: article
Abstract: A Schrödinger particle on an N-dimensional ( $$N\geqslant 2$$ N ⩾ 2 ) hypersphere of radius R is considered. The particle is subjected to the action of a force characterized by the potential $$V(\theta )=2m\omega _{1}^{2}R^{2}\tan ^{2}(\theta /2) +2m\omega _{2}^{2}R^{2}\cot ^{2}(\theta /2)$$ V ( θ ) = 2 m ω 1 2 R 2 tan 2 ( θ / 2 ) + 2 m ω 2 2 R 2 cot 2 ( θ / 2 ) , where $$0\leqslant \theta \leqslant \pi$$ 0 ⩽ θ ⩽ π is the hyperlatitude angular coordinate. In the general case when $$\omega _{1}\ne \omega _{2}$$ ω 1 ≠ ω 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 $$N=2$$ N = 2 , our results reproduce those obtained by Kazaryan et al. (Physica E 52:122, 2013). For $$N\geqslant 2$$ N ⩾ 2 arbitrary and for $$\omega _{2}=0$$ ω 2 = 0 , the results of Mardoyan and Petrosyan (J. Contemp. Phys. 48:70, 2013) for their model of an isotropic hyperspherical harmonic oscillator are recovered. The Euclidean limit for the anharmonic oscillator in question is also discussed.
Author: Radosław Szmytkowski
Institution: Gdańsk University of Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,890
OpenAlex ID: W4410082698