Coherent States of Harmonic Oscillator and Generalized Uncertainty Principle

TL;DR

This paper investigates how the Generalized Uncertainty Principle affects the dynamics and coherent states of a harmonic oscillator, revealing that quantum gravitational effects prevent perfect coherence.

Contribution

It introduces the formulation of harmonic oscillator dynamics under GUP and compares coherent states with those in standard quantum mechanics, highlighting gravitational impacts.

Findings

GUP modifies equations of motion for harmonic oscillators

Coherent states are similar in GUP and standard QM

Quantum gravity induces uncertainty that destroys perfect coherence

Abstract

In this paper dynamics and quantum mechanical coherent states of a simple harmonic oscillator are considered in the framework of Generalized Uncertainty Principle(GUP). Equations of motion for simple harmonic oscillator are derived and some of their new implications are discussed. Then coherent states of harmonic oscillator in the case of GUP are compared with relative situation in ordinary quantum mechanics. It is shown that in the framework of GUP there is no considerable difference in definition of coherent states relative to ordinary quantum mechanics. But, considering expectation values and variances of some operators, based on quantum gravitational arguments one concludes that although it is possible to have complete coherency and vanishing broadening in usual quantum mechanics, gravitational induced uncertainty destroys complete coherency in quantum gravity and it is not possible to have a monochromatic ray in principle.