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Title: Generalized uncertainty principle and self-adjoint operators

In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Neumann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are self-adjoint or not, or they have self-adjoint extensions over the given domain. In addition, a simple example of the Hamiltonian operator describing a particle in a box is given. The solutions of the boundary conditions that describe the self-adjoint extensions of the specific Hamiltonian operator are obtained.
Authors:
 [1] ;  [2] ;  [3]
  1. Department of Applied Mathematics, University of Western Ontario London, Ontario N6A 5B7 (Canada)
  2. Theoretical Physics Group, Department of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta T1K 3M4 (Canada)
  3. Theoretical Physics Group, Department of Physics, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)
Publication Date:
OSTI Identifier:
22451207
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 360; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY CONDITIONS; HAMILTONIANS; MATHEMATICAL SOLUTIONS; QUANTUM GRAVITY; QUANTUM MECHANICS; SYMMETRY; UNCERTAINTY PRINCIPLE