A class of positive quantum phase-space distributions based on antinormal ordering of the squeezed-photon annihilation and creation operators is introduced. This class of distributions, referred to as the generalized antinormally ordered distributions, is shown to be generated when the Wigner distribution is smoothed with a squeezed Gaussian wave packet. The distribution function associated with generalized antinormal ordering can thus be identified as the Husimi distribution function. The usefulness of the distributions in studies of the quantum particle dynamics is illustrated with simple examples.
A set of quasi-probability distribution functions which give the correct quantum mechanical marginal distributions of position and momentum is studied. The phase-space distribution does not have to be bilinear in the state function. The Wigner distribution is a special case. A general relationship between the phase-space distribution functions and the rule of associating classical quantities to quantum mechanical operators is derived. This allows the writing of correspondence rules at will,of which the ones presently known are particular cases. The dynamics and other properties of the generalized phase-space distribution are considered.
A new Wigner phase-space distribution function is introduced for thermal quasiparticles currently in use in thermo field dynamics. The properties of this phase-space distribution are studied and compared with those of the corresponding zero-temperature distribution. Generalized uncertainty relations are implemented in order to study the explicit spreading in phase space as a function of temperature and quantum number of the thermal excitation, thereby permitting the investigation of quantum and thermal fluctuations.