RT info:eu-repo/semantics/article
T1 Demkov–Fradkin tensor for curved harmonic oscillators
A1 Kuru, Şengül
A1 Negro, Javier
A1 Salamanca, Sergio
AB In this work, we obtain the Demkov-Fradkin tensor of symmetries for the quantum curved harmonicoscillator in a space with constant curvature given by a parameter 𝜅�. In order to construct this tensor we havefirstly found a set of basic operators which satisfy the following conditions: i) their products give symmetriesof the problem; in fact the Hamiltonian is a combination of such products; ii) they generate the space ofeigenfunctions as well as the eigenvalues in an algebraic way; iii) in the limit of zero curvature, they come intothe well known creation/annihilation operators of the flat oscillator. The appropriate products of such basicoperators will produce the curved Demkov-Fradkin tensor. However, these basic operators do not satisfyHeisenberg commutators but close another Lie algebra. As a by-product, the classical Demkov-Fradkintensor for the classical curved harmonic oscillator has been obtained by the same method. The case oftwo dimensions has been worked out in detail: the operators close a sok (4) Lie algebra; the spectrum andeigenfunctions are explicitly solved in an algebraic way and in the classical case the trajectories have beencomputed.
PB https://link.springer.com/journal/13360
YR 2025
FD 2025
LK https://uvadoc.uva.es/handle/10324/81439
UL https://uvadoc.uva.es/handle/10324/81439
LA eng
NO Eur. Phys. J. Plus (2025) 140:144
DS UVaDOC
RD 12-feb-2026