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Title: Classical and quantum dynamics in an inverse square potential

The classical motion of a particle in a 3D inverse square potential with negative energy, E, is shown to be geodesic, i.e., equivalent to the particle's free motion on a non-compact phase space manifold irrespective of the sign of the coupling constant. We thus establish that all its classical orbits with E < 0 are unbounded. To analyse the corresponding quantum problem, the Schrödinger equation is solved in momentum space. No discrete energy levels exist in the unrenormalized case and the system shows a complete “fall-to-the-center” with an energy spectrum unbounded by below. Such behavior corresponds to the non-existence of bound classical orbits. The symmetry of the problem is SO(3) × SO(2, 1) corroborating previously obtained results.
Authors:
 [1] ;  [2] ;  [3]
  1. Laboratorio de Sistemas Dinámicos, Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana, Unidad Azcapotzalco, Azcapotzalco CP 02200 D. F. (Mexico)
  2. Departamento de Física, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Apartado Postal 55-534, Iztapalapa CP 09340 D. F. (Mexico)
  3. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México (ICN-UNAM), Apartado Postal 70-543, 04510 México D F (Mexico)
Publication Date:
OSTI Identifier:
22305867
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 10; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COUPLING CONSTANTS; ENERGY LEVELS; ENERGY SPECTRA; PHASE SPACE; POTENTIALS; SCHROEDINGER EQUATION; SYMMETRY