Features of Time-independent Wigner Functions

Details Features of Time-independent Wigner Functions Features of Time-independent Wigner Functions

1997-11-25

arxiv.org/abs/hep-th/9711183v3

Phys.Rev.D58:025002,1998

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, plain LaTex, References supplemented

Scientific paper

10.1103/PhysRevD.58.025002

The Wigner phase-space distribution function provides the basis for Moyal's deformation quantization alternative to the more conventional Hilbert space and path integral quantizations. General features of time-independent Wigner functions are explored here, including the functional ("star") eigenvalue equations they satisfy; their projective orthogonality spectral properties; their Darboux ("supersymmetric") isospectral potential recursions; and their canonical transformations. These features are illustrated explicitly through simple solvable potentials: the harmonic oscillator, the linear potential, the Poeschl-Teller potential, and the Liouville potential.

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