Noncommutative quantum mechanics of simple matter systems interacting with circularly polarized gravitational waves

TL;DR

This paper explores how noncommutative quantum mechanics affects the response of simple matter systems, like free particles and harmonic oscillators, to circularly polarized gravitational waves, revealing signatures of noncommutativity in their behavior.

Contribution

It introduces a noncommutative quantum framework to analyze matter systems interacting with gravitational waves, highlighting how noncommutativity alters resonance and oscillation properties.

Findings

Signatures of coordinate noncommutativity are observed in the system's solutions.

Noncommutativity modifies the resonance point of the harmonic oscillator.

Oscillation frequency is affected by noncommutative effects.

Abstract

The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized following the prescription in \cite{ncgw1}. Standard algebraic techniques are then employed to solve the Hamiltonian of the system. The solutions, in both cases, show signatures of the coordinate noncommutativity. In the harmonic oscillator case, this signature plays a key role in altering the resonance point and the oscillation frequency of the system.