Abstract
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.
Highlights
A fundamental issue in physics is to elucidate how classical mechanics emerges from a more general theory of physics, the so-called relativistic quantum mechanics
Classical limit of quantum mechanics for a driven damped harmonic oscillator has been investigated based on the linear invariant operator
The full wave function of the system was represented in terms of the eigenstate of the linear invariant operator according to the Lewis–Riesenfeld theory [10]
Summary
A fundamental issue in physics is to elucidate how classical mechanics (or Newtonian mechanics) emerges from a more general theory of physics, the so-called relativistic quantum mechanics. While the appearing of classical mechanics as a low velocity limit of relativistic mechanics is well known, the classical limit of quantum mechanics is a subtle problem yet. There has been controversy from the early epoch of quantum mechanics concerning this limit through different ideas and thoughts [3,4,5,6,7,8,9]. Some physicists believe that quantum mechanics is not concerned with a single particle problem but an ensemble of particles, and its Z → 0 limit is not classical mechanics but classical statistical mechanics instead For more different opinions concerning the classical limit of quantum mechanics, refer in particular to Refs. For more different opinions concerning the classical limit of quantum mechanics, refer in particular to Refs. [7, 8]
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