Superintegrabilidad en Ecuaciones Differenciales de la Física

Abstract

The doctoral thesis “ Superintegrability of Differential Equations of Physics” is integrated by the investigations reported in published [1-5] and submitted [6] articles, and in contributions to specialized meetings [7, 8, 9]. The solutions for a new ring potential [1] and the radial Pöschl-Teller II [2] constructed by the Nikiforov-Uvarov method are presented in Chapter 2. The capture of an electron by a polar molecule, which has been studied in spherical and prolate spheroidal coordinates. Is the subject of Chapter 3, with emphasis on the comment [3] on Alhaidari and Bahlouli´s letter [10]. Chapter 4 presents successively the displacement operators for the particle in circular [4] and spherical [5] wells, as natural extensions to those of a one-dimensional box [11]. The recently completed work on the hydrogen atom confined by a dihedral angle [6] constitutes Chapter 5, illustrating the symmetry breaking effect by confinement on the rotational symmetry breaking effect by the confinement on the rotational symmetry around the z-axis of the superintegrable system, as well as the surviving symmetries. Chapter 6 contains a general discussion and specific conclusions on the investigated systems.