D B Fairlie and C A Manogue 1991 J. Phys. A: Math. Gen. 24 3807 doi:10.1088/0305-4470/24/16/018
The formulation of quantum mechanics in terms of phase space functions-the third equation
D B Fairlie and C A Manogue
Show affiliationsThe formalism of the Wigner distribution function is reviewed. In addition to the Liouville equation, which expresses the time rate of change of this function in terms of its Moyal bracket with the Hamiltonian, and its expression as a projection operator, a third equation is proposed with the aid of an auxiliary variable s, to which a formal solution is constructed in terms of known quantum-mechanical eigenfunctions and eigenvalues. In addition, an ab initio solution to the three equations in terms of an error function is found for the free particle in one dimension. Two views are advanced: the orthodox, that this new equation is merely a consistency requirement, and the speculative, that the measurement process has something to do with the choice of s.
- PACS
-
03.65.Vf Phases: geometric; dynamic or topological
02.50.Ng Distribution theory and Monte Carlo studies
- MSC
-
81S30 Phase space methods including Wigner distributions, etc.
- Subjects
- Dates
-
Issue 16 (21 August 1991)
-
The formulation of quantum mechanics in terms of phase space functions-the third equation
D B Fairlie and C A Manogue 1991 J. Phys. A: Math. Gen. 24 3807
-
Magnetic phase evolution in the spinel compounds Zn1−xCoxCr2O4
Brent C Melot et al 2009 J. Phys.: Condens. Matter 21 216007
-
Cross-correlation studies with seismic noise
H Hoffmann et al 2002 Class. Quantum Grav. 19 1709
-
Jets and produced particles in pp collisions from SPS to RHIC energies for nuclear applications
G G Barnaföldi et al 2001 J. Phys. G: Nucl. Part. Phys. 27 1767
-
Strange hyperon and antihyperon production from quark and string-rope matter
P Csizmadia et al 1999 J. Phys. G: Nucl. Part. Phys. 25 321
-
Strange hadrons from quark and hadron matter: a comparison
T S Biró et al 2001 J. Phys. G: Nucl. Part. Phys. 27 439
-
Hadronization of massive quark matter
T S Biró et al 1999 J. Phys. G: Nucl. Part. Phys. 25 311
-
Simple predictions from ALCORc for rehadronization of charmed quark matter
P Lévai et al 2000 New J. Phys. 2 32
-
A first map of tropical Africa's above-ground biomass derived from satellite imagery
A Baccini et al 2008 Environ. Res. Lett. 3 045011
-
Toward a Resolution of the Discrepancy between Different Estimators of Star Formation Rate
A. M. Hopkins et al. 2001 The Astronomical Journal 122 288
Users also read
What's this?- REIDEMEISTER TORSION AND THE ALEXANDER POLYNOMIAL
- What is observable in classical and quantum gravity?
- Physics of foodstuffs
= 1/2 gauge theory and its instanton moduli space from open strings in R-R backgroundRelated review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
- Spectral problems in open quantum chaos
- Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories
super-Yang–Mills*