In this work, we obtain the Demkov-Fradkin tensor of symmetries for the quantum curved harmonic
oscillator in a space with constant curvature given by a parameter 𝜅�. In order to construct this tensor we have
firstly found a set of basic operators which satisfy the following conditions: i) their products give symmetries
of the problem; in fact the Hamiltonian is a combination of such products; ii) they generate the space of
eigenfunctions as well as the eigenvalues in an algebraic way; iii) in the limit of zero curvature, they come into
the well known creation/annihilation operators of the flat oscillator. The appropriate products of such basic
operators will produce the curved Demkov-Fradkin tensor. However, these basic operators do not satisfy
Heisenberg commutators but close another Lie algebra. As a by-product, the classical Demkov-Fradkin
tensor for the classical curved harmonic oscillator has been obtained by the same method. The case of
two dimensions has been worked out in detail: the operators close a sok (4) Lie algebra; the spectrum and
eigenfunctions are explicitly solved in an algebraic way and in the classical case the trajectories have been
computed.
Exceto quando indicado o contrário, a licença deste item é descrito como CC0 1.0 Universal