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Title: On square-integrability of solutions of the stationary Schrödinger equation for the quantum harmonic oscillator in two dimensional constant curvature spaces

In this work, one provides a justification of the condition that is usually imposed on the parameters of the hypergeometric equation, related to the solutions of the stationary Schrödinger equation for the harmonic oscillator in two-dimensional constant curvature spaces, in order to determine the solutions which are square-integrable. One proves that in case of negative curvature, it is a necessary condition of square integrability and in case of positive curvature, a necessary condition of regularity. The proof is based on the analytic continuation formulas for the hypergeometric function. It is observed also that the same is true in case of a slightly more general potential than the one for harmonic oscillator.
Authors:
 [1] ;  [2]
  1. Departamento de Matemática, Universidad de Costa Rica. S.O (Costa Rica)
  2. Department of Mathematical Sciences, University of Puerto Rico, Mayagüez, Puerto Rico 00681-5000 (United States)
Publication Date:
OSTI Identifier:
22479696
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 7; Other Information: (c) 2015 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; HARMONIC OSCILLATORS; HYPERGEOMETRIC FUNCTIONS; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; POTENTIALS; SCHROEDINGER EQUATION