Related papers: The Wentzel - Kramers - Brillouin approximation me…
The framework of Wigner functions for the canonical pair angle and orbital angular momentum, derived and analyzed in 2 recent papers [H. A. Kastrup, Phys.Rev. A 94, 062113(2016) and Phys.Rev. A 95, 052111(2017)] is applied to elementary…
Classical surfaces in phase space correspond to quantum states in Hilbert space. Subsystems specify factor spaces of the Hilbert space. An entangled state corresponds semiclassically to a surface that cannot be decomposed into a product of…
The Wigner phase-space distribution function provides the basis for Moyal's deformation quantization alternative to the more conventional Hilbert space and path integral quantizations. General features of time-independent Wigner functions…
New time dependent Wigner functions for the quantum harmonic oscillator have been obtained in this work. The Moyal equation for the harmonic oscillator has been presented as the wave equation of a 2D membrane in the phase plane. The values…
In the WKB approximation the $\nabla^2S$ term in Schrodinger's equation is subordinate to the |\nabla S|^2 term. Here we study an anti-WKB approximation in which the $\nabla^2 S$ term dominates (after a guess for S is supplied). Our…
In this study, we analyze the bound-state energy spectrum of quark-antiquark systems using the semiclassical WKB approximation. We consider the Cornell potential, which combines a linear confinement term with a Coulombic interaction, and…
The Lindblad equation governs general markovian evolution of the density operator in an open quantum system. An expression for the rate of change of the Wigner function as a sum of integrals is one of the forms of the Weyl representation…
A quasi-distribution function in phase space (based on Wigner functions) is used to write down the quantum version of Boltzmann equation (Wigner-Boltzmann transport equation). The relaxation time approximation is show to be a good approach…
In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasi-probability measure. The complete sets of Wigner…
Quantum mechanics in phase space (or deformation quantization) appears to fail as an autonomous quantum method when infinite potential walls are present. The stationary physical Wigner functions do not satisfy the normal eigen equations,…
The classical limit of the Wigner-Weyl representation is used to approximate products of bound-continuum matrix elements that are fundamental to many coherent control computations. The range of utility of the method is quantified through an…
In this paper, we correct a mistake we made in [Phys. Rev. Lett. $\textbf{122}$, 190402 (2019)] and [Phys. Rev. A $\textbf{103}$, 012213 (2021)] regarding the Wigner function of the so-called smoothed Weak-Valued state (SWV state). Here…
The independent solutions of the one-dimensional Schr\"odinger equation are approximated by means of the explicit summation of the leading constituent WKB series. The continuous matching of the particular solutions gives the uniformly valid…
A new reconstruction method for Wigner function is reported for quantum tomography based on compressed sensing. By analogy with computed tomography, Wigner functions for some quantum states can be reconstructed with less measurements…
The general Weyl -- Wigner formalism in finite dimensional phase spaces is investigated. Then this formalism is specified to the case of symmetric ordering of operators in an odd -- dimensional Hilbert space. A respective Wigner function on…
Here we present complex resonance states (or Siegert states), that describe the tunneling decay of a trapped quantum particle, from an intuitive point of view which naturally leads to the easily applicable Siegert approximation method that…
Nonlocal modeling has drawn more and more attention and becomes steadily more powerful in scientific computing. In this paper, we demonstrate the superiority of a first-principle nonlocal model -- Wigner function -- in treating singular…
We show that radiation from complex and inherently random but correlated wave sources can be modelled efficiently by using an approach based on the Wigner distribution function. Our method exploits the connection between correlation…
By introducing the thermo entangled state representation, we convert the calculation of Wigner function (WF) of density operator to an overlap between "two pure" states in a two-mode enlarged Fock space. Furthermore, we derive a new WF…
We propose a simple and straightforward method based on Wronskians for the calculation of bound--state energies and wavefunctions of one--dimensional quantum--mechanical problems. We explicitly discuss the asymptotic behavior of the…