Canonical variables for the Poisson algebra of quantum moments are introduced here, expressing semiclassical quantum mechanics as a canonical dynamical system that extends the classical phase space. New realizations for up to fourth order in moments for a single classical degree of freedom and to second order for a pair of classical degrees of freedom are derived and applied to several model systems. It is shown that these new canonical variables facilitate the derivation of quantum-statistical quantities and effective potentials. Moreover, by formulating quantum dynamics in classical language, these methods result in new heuristic pictures, for instance, of tunneling, that can guide further investigations.
All Science Journal Classification (ASJC) codes
- Atomic and Molecular Physics, and Optics