RT info:eu-repo/semantics/article
T1 The Dunkl oscillator on a space of nonconstant curvature: An exactly solvable quantum model with reflections
A1 Ballesteros Castañeda, Ángel
A1 Najafizade, Amene
A1 Panahi, Hossein
A1 Hassanabadi, Hassan
A1 Dong, Shi-Hai
K1 Darboux III oscilator
K1 Dunkl derivative
K1 Curvature
K1 Integrable deformation
K1 Exact solutions
K1 Landau levels
K1 Física matemática
K1 Mathematical physics
AB We introduce the Dunkl–Darboux III oscillator Hamiltonian in N dimensions as a deformation of the Dunkl oscillator. This deformation is interpreted as the introduction of a non-constant curvature on the underlying space or, equivalently, as a quadratic position-dependent mass for the Dunkl oscillator. This new ND quantum model is shown to be exactly solvable, and its eigenvalues and eigenfunctions are explicitly presented. It is shown that in the 2D case both Darboux III and Dunkl oscillators can be coupled with a constant magnetic field, thus giving rise to two new quantum integrable systems in which the effect of the deformation and of the Dunkl derivatives on the Landau levels can be studied. Finally, the full 2D Dunkl–Darboux III oscillator is coupled with the magnetic field and shown to define an exactly solvable Hamiltonian, where the interplay between the deformation and the magnetic field is explicitly illustrated.
PB Elsevier
SN 0003-4916
YR 2024
FD 2024-01
LK http://hdl.handle.net/10259/9286
UL http://hdl.handle.net/10259/9286
LA eng
NO The authors thank the referees for thoroughly reading our manuscript and for constructive suggestions that improved the original version of this paper. A. B. has been partially supported by Agencia Estatal de Investigación (Spain) under grant PID2019-106802GB-I00/AEI/10.13039/501100011033, by the Q-CAYLE Project funded by the Regional Government of Castilla y León (Junta de Castilla y León), Spain and by the Ministry of Science and Innovation MICIN, Spain through the European Union funds NextGenerationEU (PRTR C17.I1). SH. D. acknowledges support from grant 20220355-SIP-IPN, Mexico. SH. D. started this work on sabbatical leave from IPN, Mexico. A. N. would like to thank the members of the Mathematical Physics Research Group of the University of Burgos for their kind assistance and hospitality.
DS Repositorio Institucional de la Universidad de Burgos
RD 28-jun-2024