Related papers: The Wigner Distribution
Conventional approach to quantum mechanics in phase space, (q,p), is to take the operator based quantum mechanics of Schrodinger, or and equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher…
Quantum estimation theory is a reformulation of random statistical theory with the modern language of quantum mechanics. In fact, the density operator plays a role similar to that of probability distribution functions in classical…
Quantum statistical mechanics is formulated as an integral over classical phase space. Some details of the commutation function for averages are discussed, as is the factorization of the symmetrization function used for the grand potential…
A complete solution to the problem of setting up Wigner distribution for N-level quantum systems is presented. The scheme makes use of some of the ideas introduced by Dirac in the course of defining functions of noncommuting observables and…
In our previous papers we were interested in making a reconstruction of quantum mechanics according to classical mechanics. In this paper we suspend this program for a while and turn our attention to a theme in the frontier of quantum…
After some historical remarks concerning Schroedinger's discovery of wave mechanics, we present a unified formalism for the mathematical description of classical and quantum-mechanical systems, utilizing elements of the theory of operator…
We analyze the polymer representation of quantum mechanics within the deformation quantization formalism. In particular, we construct the Wigner function and the star-product for the polymer representation as a distributional limit of the…
The Fermi g_F(x,p) function provides a phase space description of quantum mechanics conceptually different from that based on the the Wigner function W(x,p). In this paper, we show that for a peaked wave packet the g_F(x,p)=0 curve…
Wigner function is a quasi-distribution that provides a representation of the state of a quantum mechanical system in the phase space of position and momentum. In this paper we find a relation between Wigner function and appropriate…
We discuss questions pertaining to the definition of `momentum', `momentum space', `phase space', and `Wigner distributions'; for finite dimensional quantum systems. For such systems, where traditional concepts of `momenta' established for…
In 1945, Dirac attempted to develop a "formal probability" distribution to describe quantum operators in terms of two non-commuting variables, such as position x and momentum p [Rev. Mod. Phys. 17, 195 (1945)]. The resulting…
This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory.…
We propose a phase-space representation concept in terms of the Wigner function for a quantum harmonic oscillator model that exhibits the semiconfinement effect through its mass varying with the position. The new method is used to compute…
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of…
Recently, a new definition for a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum, was developed. This distribution function is…
The quantum mechanics is considered to be a partial case of the stochastic system dynamics. It is shown that the wave function describes the state of statistically averaged system $<\mathcal{S}_{st}>$, but not that of the individual…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
To unequivocally distinguish genuine quantumness from classicality, a widely adopted approach focuses on the negative values of a quasi-distribution representation as compelling evidence of nonclassicality. Prominent examples include the…
The quantum analog of the joint probability distributions describing a classical stochastic process is introduced. A prescription is given for constructing the quantum distribution associated with a sequence of measurements. For the case of…
We formulate and argue in favor of the following conjecture: There exists an intimate connection between Wigner's quantum mechanical phase space distribution function and classical Fresnel optics.