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The investigation of quantum-classical correspondence may lead to gain adeeper understanding of the classical limit of quantum theory. We develop aquantum formalism on the basis of a linear-invariant theorem, which gives anexact quantum-classical correspondence for damped oscillatory systems that areperturbed by an arbitrary force. Within our formalism, the quantum trajectoryand expectation values of quantum observables are precisely coincide with theirclassical counterparts in the case where we remove the global quantum constanth from their quantum results. In particular, we illustrate the correspondenceof the quantum energy with the classical one in detail.

Classical limit of quantum mechanics for damped driven oscillatory systems: Quantum-classical correspondence