https://doi.org/10.1140/epjp/s13360-025-06285-1
Regular Article
Particle in a spherical potential well of energy dependent depth
1
Department of Theoretical Physics, Horia Hulubei National Institute for R&D in Physics and Nuclear Engineering, Str. Reactorului 30, RO-077125, Mǎgurele, Romania
2
Academy of Romanian Scientists, Splaiul Independenţei 54, RO-050044, Bucharest, Romania
Received:
28
November
2024
Accepted:
30
March
2025
Published online:
28
April
2025
The Schrödinger equation is solved for a spherical finite well potential whose depth depends linearly on the energy. The energy spectrum is derived as a function of the well’s dimensional parameter and the slope of the energy dependence. The latter is found to have a finite domain of values which assures the existence of bound states. The evolution of the energy spectrum and the corresponding wave functions as a function of the slope parameter is exemplified within a numerical analysis. The upper limit of the slope parameter offers an infinite spectrum which is compared to the case of the infinite spherical well case. A physical application of this limiting case is presented for the shape fluctuation phenomena in atomic nuclei.
© The Author(s) 2025
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