Wigners Phase-Space Density Function

Jens Peder Dahl

The problem of two particles in a common harmonic oscillator potential interacting through harmonic oscillator forces is discussed in the Weyl–Wigner phase-space representation. The Wigner function of the system is an ordinary function of the phase-space constants of the motion. The density functional description of the system is touched upon. The functional that determines the confining harmonic potential from the particle density is also an ordinary function.

Daniel Lagolnitzer

Demircioglu, B, Abdullah Verçin

Generation of Wigner functions of Landau levels and determination of their symmetries and generic properties are achieved in the autonomous framework of deformation quantization. Transformation properties of diagonal Wigner functions under space inversion, time reversal and parity transformations are specified and their invariance under a four-parameter subgroup of symplectic transformations are established. A generating function for all Wigner functions is developed and this has been identified as the phase-space coherent state for Landau levels. Integrated forms of generating function are used in generating explicit expressions of marginal probability densities on all possible two dimensional phase-space planes. Phase-space realization of unitary similarity and gauge transformations as well as some general implications for the Wigner function theory are presented.

E. E. Perepelkin, Б. И. Садовников, Наталья Германовна Иноземцева +3 more

The paper describes the kinematic properties of quantum systems in terms of phase space. Despite the Heisenberg uncertainty principle, the consideration of quantum systems in phase space is widely used with the apparatus of quasi-probability density functions, such as the Wigner function and the gauge-invariant Weyl–Stratonovich function. The term “quasi-density” refers to the presence of phase-space regions with negative values of the probability density function and arouses interest in possible physical interpretations of such values. The kinematic properties of the systems are considered within the Wigner–Vlasov formalism, which enables to link the classical and quantum descriptions through a unified mathematical apparatus using the distribution function in phase space.

GERALD J. IAFRATE, H. L. Grubin, David K. Ferry