2026-04-30T04:54:47Zhttps://uvadoc.uva.es/oai/request

oai:uvadoc.uva.es:10324/839432026-04-08T09:08:08Zcom_10324_1159com_10324_931com_10324_894col_10324_1310

Jimenez Trejo, G. Negro Vadillo, Francisco Javier Nieto Calzada, Luis Miguel Cruz y Cruz, Sara 2026-04-07T12:06:17Z 2026-04-07T12:06:17Z 2026 Annals of Physics, 2026, vol. 489, p. 170460 0003-4916 https://uvadoc.uva.es/handle/10324/83943 10.1016/j.aop.2026.170460 170460 Annals of Physics 489 Producción Científica 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. Esta investigación fue financiada por el Ministerio de Ciencia e Innovación, la Junta de Castilla y León y Unión Europea-Next Generation EU/MICIU/Plan de Recuperacion, Transformacion Resiliencia - Proyecto Q-CAYLE (PRTRC17.11) Ministerio de Ciencia e Innovación - MICIU/AEI/10.13039/501100011033 (proyecto PID2023-148409NB-I00) Instituto Politécnico Nacional, México (SIP20253949) y (SIIS/DRI/DII/DMI/0051-1/2025) La Secretaría de Ciencia, Humanidades, Tecnología e Innovación, México (SECIHTI) (CBF-25-1-2875, CF19-15022) Junta de Castilla Leon (Consejería de Educación) y de los Fondos FEDER (Referencia: CLU-2023-1-05) application/pdf eng Elsevier info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/4.0/ © 2026 The Author(s) Atribución 4.0 Internacional Helmholtz equation Geometric symmetries Dynamical symmetries Separation of variables Polar and parabolic coordinates Makarov potential 12 Matemáticas Polar and parabolic separable extensions of the two dimensional Helmholtz equation in free space: From geometric to dynamical symmetries info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion https://www.sciencedirect.com/science/article/pii/S0003491626001193 SI