Noncommutative quantum mechanics of a test particle under linearized gravitational waves

TL;DR

This paper explores the quantum behavior of a test particle in noncommutative space influenced by linearized gravitational waves, revealing signatures of noncommutativity through exact solutions and expectation values.

Contribution

It introduces a method to quantize the Hamiltonian of a particle in noncommutative space under gravitational waves and provides exact solutions demonstrating noncommutative effects.

Findings

Signatures of noncommutative space in quantum dynamics

Exact solutions showing noncommutative effects

Expectation values indicating quantum spacetime noncommutativity

Abstract

We consider the quantum dynamics of a test particle in noncommutative space under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. A prescription for quantizing the classical Hamiltonian for the interaction of gravitational wave with matter in noncommutative space is proposed. The Hamiltonian (and hence the system) is then exactly solved by using standard algebraic methods. The solutions show prominent signatures of the noncommutative nature of space. Computation of the expectation value of the particle's position reveals the inherent quantum nature of spacetime noncommutativity.