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

TL;DR

This paper develops a quantum formalism that precisely links quantum and classical descriptions of damped driven oscillatory systems, clarifying the classical limit of quantum mechanics through exact correspondence.

Contribution

It introduces a linear-invariant quantum formalism that achieves exact quantum-classical correspondence for damped oscillatory systems under arbitrary forces.

Findings

Quantum trajectories match classical ones when quantum constant is removed.

Quantum expectation values coincide with classical observables.

Quantum energy corresponds closely with classical energy.

Abstract

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