Quantum dynamics for general time-dependent three coupled oscillators based on an exact decoupling

Abstract

Quantum dynamics of general time-dependent three coupled oscillators is investigated through an alternative approach based on decoupling of them using the unitary transformation method. From a first unitary transformation, the quantal Hamiltonian of the complicated original system is transformed to an equal but a simple one associated with the three coupled oscillators of which masses are unity. To diagonalize the transformed Hamiltonian, we transform the Hamiltonian once again by introducing a new unitary operator. This transformation corresponds to a three-dimensional rotation parameterized by Euler angles. Through these procedures, the coupled oscillatory subsystems are completely decoupled. The importance of this decouplement is that it enables us to develop exact theory for mechanical treatment of the originally-coupled systems without any restriction in the form of time-varying parameters.