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Title: Quantization of a particle on a two-dimensional manifold of constant curvature

The formulation of quantum mechanics on spaces of constant curvature is studied. It is shown how a transition from a classical system to the quantum case can be accomplished by the quantization of the Noether momenta. These can be determined by means of Lie differentiation of the metric which defines the manifold. For the metric examined here, it is found that the resulting Schrödinger equation is separable and the spectrum and eigenfunctions can be investigated in detail.
Authors:
 [1]
  1. Department of Mathematics, University of Texas, Edinburg, Texas 78540 (United States)
Publication Date:
OSTI Identifier:
22305855
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; EIGENFUNCTIONS; MATHEMATICAL MANIFOLDS; METRICS; PARTICLES; QUANTIZATION; QUANTUM MECHANICS; SCHROEDINGER EQUATION; TWO-DIMENSIONAL CALCULATIONS