Coherent States in Gravitational Quantum Mechanics

TL;DR

This paper constructs and analyzes coherent states within a gravitationally modified quantum framework, revealing entropy reduction due to minimal length effects and potential experimental detectability of Planck-scale phenomena.

Contribution

It introduces a method to derive exact coherent states in GUP-modified quantum mechanics, connecting quantum gravity theories with observable quantum states.

Findings

Entropy decreases with minimal length

Exact coherent states are constructed in GUP framework

Potential for detecting Planck-scale effects experimentally

Abstract

We present the coherent states of the harmonic oscillator in the framework of the generalized (gravitational) uncertainty principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity, and black-hole physics and implies a minimal measurable length. Using a recently proposed formally self-adjoint representation, we find the GUP-corrected Hamiltonian as a generator of the generalized Heisenberg algebra. Then following Klauder's approach, we construct exact coherent states and obtain the corresponding normalization coefficients, weight functions, and probability distributions. We find the entropy of the system and show that it decreases in the presence of the minimal length. These results could shed light on possible detectable Planck-scale effects within recent experimental tests.