A Note on Coherent States with Quantum Gravity Effects

TL;DR

This paper explores the effects of the Generalized Uncertainty Principle, incorporating minimal length and maximal momentum, on quantum harmonic oscillators and their coherent states, revealing new quantum behavior modifications.

Contribution

It introduces a study of coherent states within the GUP framework considering both minimal length and maximal momentum, extending previous quantum mechanics models.

Findings

Modified energy spectrum for harmonic oscillator

Altered properties of coherent states under GUP

Insights into quantum behavior with quantum gravity effects

Abstract

Existence of a minimal measurable length and an upper bound for the momentum fluctuations are the casting reasons for generalization of uncertainty principle and then reformulation of Hilbert space representation of quantum mechanics. In this paper, we study the consequences of the Generalized Uncertainty Principle (GUP) in the presence of both minimal length and maximal momentum. We consider a simple harmonic oscillator in the framework of GUP by introducing it's energy eigenstates and energy spectrum. Investigation of coherent states for a generalized harmonic oscillator and it's generic behavior are the other topics in our study.