Generalized Uncertainty Principle and Self-Adjoint Operators

Abstract

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-Newmann 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.

v1: 22 pages, LaTeX, revtex4; v2: 19 pages, minor corrections, to appear in Annals of Physics

References in corpus (5)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Lorentz invariance with an invariant energy scale
• Quantum Spacetime Phenomenology
• Discreteness of Space from the Generalized Uncertainty Principle
• Self-adjoint extensions of operators and the teaching of quantum mechanics

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