Abstract
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. The 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 Pöschl-Teller potential, and the Liouville potential.
| Original language | English (US) |
|---|---|
| Number of pages | 1 |
| Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |
| Volume | 58 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jan 1 1998 |
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ASJC Scopus subject areas
- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)
Cite this
Features of time-independent Wigner functions. / Curtright, Thomas; Fairlie, David; Zachos, Cosmas.
In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 58, No. 2, 01.01.1998.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Features of time-independent Wigner functions
AU - Curtright, Thomas
AU - Fairlie, David
AU - Zachos, Cosmas
PY - 1998/1/1
Y1 - 1998/1/1
N2 - 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. The 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 Pöschl-Teller potential, and the Liouville potential.
AB - 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. The 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 Pöschl-Teller potential, and the Liouville potential.
UR - http://www.scopus.com/inward/record.url?scp=85038976783&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85038976783&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.58.025002
DO - 10.1103/PhysRevD.58.025002
M3 - Article
AN - SCOPUS:85038976783
VL - 58
JO - Physical review D: Particles and fields
JF - Physical review D: Particles and fields
SN - 0556-2821
IS - 2
ER -