Quantum mechanics of a charged particle in a background magnetic field interacting with linearized gravitational waves

TL;DR

This paper explores the quantum behavior of a charged particle in a magnetic field affected by gravitational waves, revealing potential resonance tuning through magnetic field adjustments.

Contribution

It introduces a quantum model for a charged particle in electromagnetic and gravitational wave backgrounds, solving the Hamiltonian analytically in the long wavelength and low-velocity limit.

Findings

Quantum solutions align with classical predictions

Resonance can be achieved by tuning magnetic field frequency

Demonstrates interplay between electromagnetic and gravitational effects

Abstract

We consider the dynamics of a charged particle interacting with background electromagnetic field under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. Following the prescription in \cite{speli}, the system is quantized and the Hamiltonian is then solved by using standard algebraic iterative methods. The solution is in conformity with the classical analysis and shows the possibility of tuning the frequency by changing the magnetic field to set up resonance.