Planck scale Corrections to the Harmonic Oscillator, Coherent and Squeezed States
General Relativity and Quantum Cosmology
2017-09-13 v2 High Energy Physics - Theory
Quantum Physics
Abstract
The Generalized Uncertainty Principle (GUP) is a modification of Heisenberg's Principle predicted by several theories of Quantum Gravity. It consists of a modified commutator between position and momentum. In this work we compute potentially observable effects that GUP implies for the harmonic oscillator, coherent and squeezed states in Quantum Mechanics. In particular, we rigorously analyze the GUP-perturbed harmonic oscillator Hamiltonian, defining new operators that act as ladder operators on the perturbed states. We use these operators to define the new coherent and squeezed states. We comment on potential applications.
Keywords
Cite
@article{arxiv.1704.08198,
title = {Planck scale Corrections to the Harmonic Oscillator, Coherent and Squeezed States},
author = {Pasquale Bosso and Saurya Das and Robert B. Mann},
journal= {arXiv preprint arXiv:1704.08198},
year = {2017}
}
Comments
15 pages, 3 figures, accepted in Physical Review D