The dynamics of time-dependent coupled oscillator model for the chargedparticle motion subjected to a time-dependent external magnetic field isinvestigated. We used canonical transformation approach for the classicaltreatment of the system, whereas unitary transformation approach is used whenmanaging 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 sumof two independent harmonic oscillators which have time-dependent frequencies.We therefore easily identified the wave functions in the transformed systemwith the help of invariant operator of the system. The full wave functions inthe original system is derived from the inverse unitary transformation of thewave functions associated to the transformed system.
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