# Planck scale Corrections to the Harmonic Oscillator, Coherent and Squeezed States

## TL;DR

This paper investigates how the Generalized Uncertainty Principle (GUP), a quantum gravity prediction, affects harmonic oscillator states, introducing new operators and states with potential observable implications.

## Contribution

It provides a rigorous analysis of GUP-perturbed harmonic oscillator Hamiltonian and defines new coherent and squeezed states incorporating quantum gravity effects.

## Key findings

- Derived modified ladder operators for GUP-affected harmonic oscillator
- Defined new coherent and squeezed states under GUP modifications
- Discussed potential observable effects of GUP in quantum systems

## 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.