Time-dependent coupled oscillator model for charged particle motion in the presence of a time varyingmagnetic field

TL;DR

This paper models the motion of charged particles in a time-varying magnetic field using a coupled oscillator framework, employing classical and quantum transformations to simplify and solve the system.

Contribution

It introduces a unified approach using canonical and unitary transformations to analyze the classical and quantum dynamics of charged particles in time-dependent magnetic fields.

Findings

Transformation to independent harmonic oscillators simplifies analysis.

Wave functions are explicitly derived for both classical and quantum cases.

The approach provides a clear method to handle time-dependent magnetic systems.

Abstract

The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the system, whereas unitary transformation approach is used when managing the system in the framework of quantum mechanics. For both approaches, the original system is transformed to a much more simple system that is the sum of two independent harmonic oscillators which have time-dependent frequencies. We therefore easily identified the wave functions in the transformed system with the help of invariant operator of the system. The full wave functions in the original system is derived from the inverse unitary transformation of the wave functions associated to the transformed system.