In this letter, the ”number-phase entropic uncertainty relation” and the ”number-phase Wigner function” of generalized coherent states associated to a few solvable quantum systems with nondegenerate spectra are studied. We also investigate time evolution of ”number-phase entropic uncertainty” and ”Wigner function” of the considered physical systems with the help of temporally stable Gazeau-Klau...

The Wigner formulation of quantum mechanics is a very intuitive approach which allows the comprehension and prediction of quantum mechanical phenomena in terms of quasidistribution functions. In this review, our aim is to provide a detailed introduction to this theory along with a Monte Carlo method for the simulation of time-dependent quantum systems evolving in a phase-space. This work consis...

Additivity of Breit-Wigner phases has been proposed to describe interfering resonances in partial waves in ππ scattering. This assumption leads to an expression for partial wave amplitudes that involves products of Breit-Wigner amplitudes. We show that this expression is equivalent to a coherent sum of Breit-Wigner amplitudes with specific complex coefficients which depend on the resonance para...

The Wigner-WeylMoyal approach to Quantum Mechanics is recalled, and similarities to classical probability theory emphasised. The Wigner distribution function is generalised and viewed as a construction of a bosonic object, a target space co-ordinate, for example, in terms of a bilinear convolution of two fermionic objects, e.g. a quark antiquark pair. This construction is essentially non-local,...

Wigner function(WF), a quasi-probability distribution in phase space, was first introduced to describe quantum state in quantum mechanics by E. P. Wigner[1]. And later, it was extended to classical optics and signal processing. Since its birth, a great number of applications have been conducted in different fields. As for the original quantum case, like a continuous onedimensional quantum syste...

We calculate the Wigner distribution function for the Calogero-Sutherland system which consists of harmonic and inverse-square interactions. The Wigner distribution function is separated out into two parts corresponding to the relative and center-of-mass motions. A general expression for the relative Wigner function is obtained in terms of the Laguerre polynomials by introducing a new identity ...

The possibility of constructing a complete, continuous Wigner function for any quantum system has been a subject of investigation for over 50 years. A key system that has served to illustrate the difficulties of this problem has been an ensemble of spins. Here we present a general and consistent framework for constructing Wigner functions exploiting the underlying symmetries in the physical sys...

Random matrix theory (RMT) has wide applications in various areas of science. It can be traced back to sample covariance matrices studied by J. Wishart in data analysis in 1920s1930s. In 1951, E. Wigner associated the energy levels of heavy-nuclei atoms with Hermitian matrices with i.i.d entries. To simplify the complex Hamiltonians of heavy-nuclei atoms, Wigner introduced the ensemble of real ...

The relativistic semi-classical approximation for a free massive particle is studied using the Wigner-Weyl formalism. A non-covariant Wigner function is defined using the Newton-Wigner position operator. The perturbative solution for the time evolution is found. Causality is found to be perturbatively respected. 1 1 Introduction. The Wigner-Weyl formalism [1] offers a classical-like formulation...