Incollection,
Schrodinger's equation in the phase space formulation of quantum mechanics
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
The phase space formulation of quantum mechanics has become an important tool in modern quantum statistical physics. A key role in this approach is played by the Wigner function, which is the representative of the density operator. However, in the usual formulation as pioneered by Wigner, Groenewold, Moyal and others, there is no phase space representative of the state vector. This can be overcome by using the two-sided Wigner function with the right-hand member kept fixed. This has many of the properties desired for a phase space wavefunction. In particular, it satisfies Schrodinger's equation in phase space, and the usual Wigner function can be expressed as a bilinear form in terms of this wavefunction and its conjugate, with the help of the star-product. Different choices of the fixed right-hand member lead to different possible phase space wavefunctions. Choosing a coherent state for the right-hand member leads to an unexpected connection between the Bargmann and phase space formulations of quantum mechanics.
Tags
- bargmann
- equation
- function
- mechanics
- phase
- quantum
- representation
- schrodinger
- space
- statphys23
- topic-8
- wigner
