https://doi.org/10.1140/epjp/s13360-021-01806-0
Regular Article
Quasi-exactly solvable Schrödinger equation for a modified ring-shaped harmonic oscillator potential
1
Laboratoire d’Ingénierie des Connaissances et Sécurité Informatique, Département des Mathématiques, et Informatique, Université Abbes Laghrour Khenchela, Khenchela, Algeria
2
Laboratoire des Systémes Dynamiques et Contrôle, Département des Mathématiques et informatique, Université Larbi Ben M’hidi, Oum El - Bouaghi, Algeria
3
Laboratoire des Sciences Naturelles et Matériaux, Centre Universitaire Abdelhafid Boussouf, Mila, Algeria
4
Département des Mathématiques et Informatique, Inst. des Sciences et Technologie, Centre Universitaire Abdelhafid Boussouf, Mila, Algeria
b
b.boudjedaa@centre-univ-mila.dz
Received:
5
May
2021
Accepted:
26
July
2021
Published online:
4
August
2021
The exact solutions of the Schrödinger equation for the quasi-exactly solvable (QES) modified ring-shaped harmonic oscillator potential are presented. Using the change of variables to the cylindrical coordinates and with the separation of variables method, the problem is transformed to the study of the solutions of the biconfluent Heun equation. Bound states and the associated energy eigenvalues are obtained explicitly.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
