Born-Jordan quantization. Theory and applications

DOI10.1007/978-3-319-27902-2zbMath1338.81014OpenAlexW2264764734MaRDI QIDQ908100

Maurice A. De Gosson

Publication date: 2 February 2016

Published in: Fundamental Theories of Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-27902-2

zbMATH Keywords

Weyl quantizationpseudo-differential operatorsBorn-Jordan quantizationmatrix mechanicswave mechanics

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Research exposition (monographs, survey articles) pertaining to quantum theory (81-02) Geometry and quantization, symplectic methods (81S10) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Deformation quantization, star products (53D55) Geometric quantization (53D50)

Related Items

Born-Jordan and Weyl quantizations of the 2D anisotropic harmonic oscillator ⋮ Recent developments in combinatorial aspects of normal ordering ⋮ Continuity properties for Born-Jordan operators with symbols in Hörmander classes and modulation spaces ⋮ Two-mode squeezed state quantisation and semiclassical portraits ⋮ Phase spaces, parity operators, and the Born-Jordan distribution ⋮ Generalized Born-Jordan distributions and applications ⋮ Observing quantum trajectories: From Mott's problem to quantum Zeno effect and back ⋮ Born-Jordan pseudodifferential operators with symbols in the Shubin classes ⋮ A refinement of the Robertson-Schrödinger uncertainty principle and a Hirschman-Shannon inequality for Wigner distributions ⋮ A Wiener Tauberian theorem for operators and functions ⋮ Quantum Harmonic Analysis of the Density Matrix ⋮ Linear Perturbations of the Wigner Transform and the Weyl Quantization ⋮ From classical to quantum models: the regularising Rôle of integrals, symmetry and probabilities ⋮ On the Symplectic Covariance and Interferences of Time-Frequency Distributions ⋮ Generalized Weyl quantization and time ⋮ Born-Jordan pseudodifferential operators and the Dirac correspondence: beyond the Groenewold-van Hove theorem ⋮ Almost diagonalization of \(\tau \)-pseudodifferential operators with symbols in Wiener amalgam and modulation spaces ⋮ Mixed-state localization operators: Cohen's class and trace class operators ⋮ Quantizations of the classical time of arrival and their dynamics ⋮ Characterization of smooth symbol classes by Gabor matrix decay ⋮ Bypassing the Groenewold–van Hove obstruction on ${{\mathbb{R}}}^{2n}$: a new argument in favor of Born–Jordan quantization ⋮ Generalized Susskind–Glogower coherent states ⋮ Signal Analysis Using Born–Jordan-Type Distributions ⋮ Quantum and semi-classical aspects of confined systems with variable mass ⋮ Dynamics of the τ-Wigner distribution function

This page was built for publication: Born-Jordan quantization. Theory and applications