Related papers: Hydrogen atom in phase space: The Wigner represent…
The coherence properties of the classical waves are discussed in terms of the Cauchy problem for the wave equation, and of a discrete representation by an ensemble of Hamiltonian systems. Wave quanta are related to specific "action fields",…
This note discusses the Wigner function representation from the standpoint of establishing a holography-like correspondence between the descriptions of a generic quantum system in the phase space ('bulk') picture versus its spacetime…
The evolution of the discrete Wigner function is formally similar to a probabilistic process, but the transition probabilities, like the discrete Wigner function itself, can be negative. We investigate these transition probabilities, as…
The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the…
We introduce a numerical method to simulate nonlinear open quantum dynamics of a particle in situations where its state undergoes significant expansion in phase space while generating small quantum features at the phase-space Planck scale.…
The intention of this paper is to provide solutions to commutative relations relevant to calculations regarding the hydrogen atom (or similar monoelectronic systems). Though exact solutions exist to these systems, the value to approximation…
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…
We define a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum. The distribution function is thus defined on discrete…
In every state of a quantum particle, Wigner's quasidistribution is the unique quasidistribution on the phase space with the correct marginal distributions for position, momentum, and all their linear combinations.
We show that a highly-excited energy eigenfunction $\psi_{nlm}(\vec{r})$ of hydrogen atom can be approximated as an equal-weight superposition of classical elliptic orbits with energy $E_n$ and angular momentum $L=\sqrt{l(l+1)}\hbar$, and…
We present the application of variational-wavelet analysis to numerical/analytical calculations of Wigner functions in (nonlinear) quasiclassical beam dynamics problems. (Naive) deformation quantization and multiresolution representations…
We substantiate the need for account of the proper electromagnetic field of the electron in the canonical problem of hydrogen in relativistic quantum mechanics. From mathematical viewpoint, the goal is equivalent to determination of the…
In this article we introduce a quasiprobability distribution of work that is based on the Wigner function. This construction rests on the idea that the work done on an isolated system can be coherently measured by coupling the system to a…
The hydrogen atom theory is developed for the de Sitter and anti de Sitter spaces on the basis of the Klein-Gordon-Fock wave equation in static coordinates. In both models, after separation of the variables, the problem is reduced to the…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
Using the quadratic transformation and the generating function method we Perform the Fourier transformation of the wave function of coordinates of hydrogen atom and we find the analytic expression of the wave function in momentum space. We…
We propose a complete tomographic reconstruction of any vortex state carrying orbital angular momentum. The scheme determines the angular probability distribution of the state at different times under free evolution. To represent the…
We present a geometrical way of understanding the dynamics of wavefunctions in a free space, using the phase-space formulation of quantum mechanics. By visualizing the Wigner function, the spreading, shearing, the so-called "negative…
Thanks to the Dirac equation, the hydrogen-like atom at high $Z$ offers a precise model of relativistic bound state, allowing to test properties of unpolarized and polarized structure functions analogous to the hadronic ones, in particular:…
The Wigner function formalism has been applied to the analysis of elastic scattering processes. The new element of known formalism is the choice of the phase space on which the Wigner function is defined. This phase space is 4-dimensional…