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

Abstract

Read online

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 ℏ has been removed from their quantum results. In particular, I have illustrated the correspondence of the quantum energy with the classical one in detail.

Keywords

• quantum–classical correspondence
• classical limit
• Caldirola–Kanai Hamiltonian
• quantum energy
• invariant operator