Canonical Transformations for Time Evolution and Their Representation in Wigner Distribution Phase Space

✍ Scribed by Marcos Moshinsky; Anju Sharma

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 129 KB
• Volume: 282
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.2000.6038

✦ Synopsis

The classical evolution in time of a point in phase space associated with a Hamiltonian is given by a canonical transformation. In the configuration space of 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.