Related papers: Quantum wavepackets: Proofs (almost) without words
Wave-like partial differential equations occur in many engineering applications. Here the engineering setup is embedded into the Hilbert space framework of functional analysis of modern mathematical physics. The notion wave-like is a…
We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties…
We propose a very simple experimental setup to measure, via photon counting, the overlap of the Wigner functions characterizing two single mode light beams. We show that this scheme can be applied to determine directly the phase space…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…
We analyze an experiment in which a thin wire is scanned across the overlap of two in phase photon beams. We find that unless the wire induces the formation of an interference pattern, the complementarity inequality is violated. Quantum…
There are reasons to doubt that making sense of the wave function (other than as a probability algorithm) will help with the project of making sense of quantum mechanics. The consistency of the quantum-mechanical correlation laws with the…
One of the most prominent quasiprobability functions in quantum mechanics is the Wigner function that gives the right marginal probability functions if integrated over position or momentum. Here we depart from the definition of the…
Within a plane-wave approximation in scattering, an incoming wave packet's Wigner function stays everywhere positive, which obscures such purely quantum phenomena as non-locality and entanglement. With the advent of the electron microscopes…
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…
In contrast to classical physics, the language of quantum mechanics involves operators and wave functions (or, more generally, density operators). However, in 1932, Wigner formulated quantum mechanics in terms of a distribution function…
The short time dynamics of a quantum Brownian particle in a harmonic potential is studied in the phase space. An exact non-Markovian analytic approach to calculate the time evolution of the Wigner function is presented. The dynamics of the…
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…
Based on the dispersion chain of the Vlasov equations, the paper considers the construction of a new chain of equations of quantum mechanics of high kinematical values. The proposed approach can be applied to consideration of classical and…
We provide an introduction into the formulation of non-relativistic quantum mechanics using the Wigner phase-space distribution function and apply this concept to two physical situations at the interface of quantum theory and general…
With approaching quantum/noncommutative models for the deep microscopic spacetime in mind, and inspired by our recent picture of the (projective) Hilbert space as the model of physical space behind basic quantum mechanics, we reformulate…
Representations of the Poincar\'{e} symmetry are studied by using a Hilbert space with a phase space content. The states are described by wave functions ( quasi amplitudes of probability) associated with Wigner functions (quasi probability…
This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that…
A new version of hidden variables theory founded on the generalisation of world's geometry is proposed. The quantum-mechanical motion as the motion in some "inner space", which has a structure of the integrable Weyl space is examined.…
This work is an extended version of the paper arXiv:0803.2669v1[math-ph], in which the main results were announced. We consider certain classical diffusion process for a wave function on the phase space. It is shown that at the time of…
This work explores the intersection of quantum mechanics and curved spacetime by employing the Wigner formalism to investigate quantum systems in the vicinity of black holes. Specifically, we study the quantum dynamics of a probe particle…