RT info:eu-repo/semantics/article
T1 Polar and parabolic separable extensions of the two dimensional Helmholtz equation in free space: From geometric to dynamical symmetries
A1 Jimenez Trejo, G.
A1 Negro Vadillo, Francisco Javier
A1 Nieto Calzada, Luis Miguel
A1 Cruz y Cruz, Sara
K1 Helmholtz equation
K1 Geometric symmetries
K1 Dynamical symmetries
K1 Separation of variables
K1 Polar and parabolic coordinates
K1 Makarov potential
K1 12 Matemáticas
AB We analyze two-dimensional systems related to the Helmholtz equation that allow separation of variables in both polar and parabolic coordinates. We pay special attention to the symmetry algebras involved in the separation of variables. We show how the modification of symmetry operators can lead from purely geometric symmetries to other dynamical ones, that is, from free systems to interacting systems, with the addition of potentials, which in our case are of two types: Kepler–Coulomb and Makarov. We also calculate the spectrum and associated eigenfunctions of the corresponding quantum mechanical systems, and we present a discussion of naturally separable classical systems, including the analysis of different types of trajectories. A discussion of the global properties of polar and parabolic coordinates is included, the relevance of which is demonstrated in the spectral and classical properties of these systems.
PB Elsevier
SN 0003-4916
YR 2026
FD 2026
LK https://uvadoc.uva.es/handle/10324/83943
UL https://uvadoc.uva.es/handle/10324/83943
LA eng
NO Annals of Physics, 2026, vol. 489, p. 170460
NO Producción Científica
DS UVaDOC
RD 07-abr-2026