2026-04-27T21:55:04Zhttps://uvadoc.uva.es/oai/request

oai:uvadoc.uva.es:10324/814422026-04-17T06:48:26Zcom_10324_1159com_10324_931com_10324_894col_10324_1310

SO(2,2) representations in polar coordinates and Pöschl-Teller potentials Blázquez Villalobos, María del Carmen Negro Vadillo, Francisco Javier Mathematical physics Variables (Matemáticas) This work is devoted to show the interest of polar coordinates in the description of some unitary irreducible representations (or uir’s) of the SO(2, 2) group where the support space are functions on the three dimensional pseudosphere H2,2R . We will show that the differential equations associated to such uir’s can be interpreted as quantum systems including centrifugal terms; in our case these equations lead to one-dimensional Pöschl-Teller systems. The solutions to these equations are computed and the uir’s are characterized in terms of polar coordinates. We will also discuss briefly the more standard pseudospherical coordinates onH2,2 R in order to appreciate some of the differences. We will consider as well the (maximally superintegrable) free classical systems defined on the real pseudosphere H2,2 R symmetric under SO(2, 2). The constants of motion are found and they are applied to find some bounded (therefore periodic) and unbounded orbits also in terms of polar coordinates. 2026-01-13T16:10:43Z 2026-01-13T16:10:43Z 2024 info:eu-repo/semantics/article Journal of Physics A: Mathematical and Theoretical, 2024, vol. 57, nº. 19, 195204, 22 pp. 1751-8113 https://uvadoc.uva.es/handle/10324/81442 10.1088/1751-8121/ad3d45 195204 19 Journal of Physics A: Mathematical and Theoretical 57 1751-8121 spa info:eu-repo/semantics/openAccess IOP SI