Canonical transformations for time evolution and their representation in Wigner distribution phase space

摘要

The classical evolution in time of a paint in phase space associated with a Hamiltonian is given by a canonical transformation. In the configuration space or quantum mechanics the corresponding evolution is determined by the time-dependent Green function. Using the latter to obtain the appropriate Wigner distribution. We derive a kernel in phase space that gives us the evolution of the probability density associated with the canonical transformation. We illustrate our analysis through several simple examples. (C) 2000 Academic Press. [References: 17]