Generalized uncertainty principle and self-adjoint operators

Journal Article · Tue Sep 15 00:00:00 EDT 2015 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2015.04.033· OSTI ID:22451207

Balasubramanian, Venkat ^[1]; Das, Saurya ^[2]

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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)

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.

• OSTI ID: 22451207
• Journal Information: Annals of Physics, Vol. 360; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
HAMILTONIANS
MATHEMATICAL SOLUTIONS
QUANTUM GRAVITY
QUANTUM MECHANICS
SYMMETRY
UNCERTAINTY PRINCIPLE