Noncommutative quantum mechanics of a test particle under linearly polarized gravitational waves

Abstract

We consider the quantum dynamics of a test particle first with no potential and then with hermonic oscillator potential in noncommutative space under the influence of a passing linearized gravitational wave in the long wave-length and low-velocity limit. A prescription for quantizing the classical Hamiltonian for these systems is proposed. While both the solutions show noncommutative signatures, for the hermonic oscillator case a resonance scenario is found. We expect this noncommutative signature to show up as some noise source in the GW detection experiments since the recent phenomenological upper-bounds set on spatial noncommutative parameter implies a length-scale comparable to the length-variations due to the passage of gravitational waves, detectable in the present day GW detectors.