Generalized Uncertainty Principle and Self-Adjoint Operators
High Energy Physics - Theory
2015-05-26 v2 General Relativity and Quantum Cosmology
High Energy Physics - Phenomenology
Quantum Physics
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.
Cite
@article{arxiv.1404.3962,
title = {Generalized Uncertainty Principle and Self-Adjoint Operators},
author = {Venkat Balasubramanian and Saurya Das and Elias C. Vagenas},
journal= {arXiv preprint arXiv:1404.3962},
year = {2015}
}
Comments
v1: 22 pages, LaTeX, revtex4; v2: 19 pages, minor corrections, to appear in Annals of Physics