Classical Limit of Quantum Mechanics for Damped Driven Oscillatory Systems: Quantum-Classical Correspondence

The investigation of quantum-classical correspondence may lead to gaining a deeper understanding of the classical limit of quantum theory. I have developed a quantum formalism on the basis of a linear invariant theorem, which gives an exact quantum-classical correspondence for damped oscillatory systems perturbed by an arbitrary force. Within my formalism, the quantum trajectory and expectation values of quantum observables precisely coincide with their classical counterparts in the case where the global quantum constant PLANCK CONSTANT OVER TWO PI has been removed from their quantum results. In particular, I have illustrated the correspondence of the quantum energy with the classical one in detail.

Automated summary

The researcher has developed a quantum formalism based on a linear invariant theorem to provide an exact quantum-classical correspondence for damped oscillatory systems perturbed by arbitrary forces, removing the global quantum constant from their quantum results. The study specifically illustrates the precise correspondence of quantum energy with classical energy.