Quantum Mechanics in Phase Space

Abstract

Ever since Werner Heisenberg's 1927 paper on uncertainty, there has been considerable hesitancy in simultaneously considering positions and momenta in quantum contexts, since these are incompatible observables. But this persistent discomfort with addressing positions and momenta jointly in the quantum world is not really warranted, as was first fully appreciated by Hilbrand Groenewold and José Moyal in the 1940s. While the formalism for quantum mechanics in phase space was wholly cast at that time, it was not completely understood nor widely known --- much less generally accepted --- until the late 20th century.

A brief history of deformation quantization, ca 1930-1960, with some elementary illustrations of the theory

Cited by in corpus (70)

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• Towards a Cosmology with Minimal Length and Maximal Energy
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• Contact Geometry and Quantum Mechanics
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• Electron dynamics in noncommutative geometry with magnetic field and Zitterbewegung phenomenon
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• Topological invariant in terms of the Green functions for the Quantum Hall Effect in the presence of varying magnetic field
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• A Note on Bloch theorem
• Dynamical transition from localized to uniform scrambling in locally hyperbolic systems
• Quantization: History and Problems
• Vacuum energy and the cosmological constant problem in $\kappa$-Poincaré invariant field theories
• Epistemic Horizons and the Foundations of Quantum Mechanics
• Local realistic interpretation of entangled photon pairs in the Weyl-Wigner formalism
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• Study on a Phase Space Representation of Quantum Theory
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• Dispersion Operators Algebra and Linear Canonical Transformations
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• Momentum Space Topology and Non-Dissipative Currents
• A Wigner distribution function for finite oscillator systems
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• Tomography from collective measurements
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• Evolution equation for multi-photon states in turbulence
• Efficient computations of quantum canonical Gibbs state in phase space
• Toolbox for non-classical state calculations
• Wigner representation of the rotational dynamics of rigid tops
• Anomalous fractional quantum Hall effect and multi-valued Hamiltonians
• The Morse potential and phase-space quantum mechanics
• Nonlinear interferometry in all spatiotemporal degrees of freedom
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• Phase space holography with no strings attached
• Quantum and Relativistic corrections to Maxwell-Boltzmann ideal gas model from a Quantum Phase Space approach
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• Wigner current in multidimensional quantum billiards
• Wigner - Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field
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• Wigner function dynamics with boundaries expressed as convolution
• Wigner functional theory for quantum optics
• Coherent states for dispersive pseudo-Landau-levels in strained honeycomb lattices
• Lorentzian Vacuum Transitions with a Generalized Uncertainty Principle
• Covariant operator bases for continuous variables
• Perturbation solutions of the semiclassical Wigner equation
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• Classical Propagation in the Quantum Inverted Oscillator
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• Stimulated parametric down-conversion for spatiotemporal metrology
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• Analytic representations with Theta functions for systems on Z(d) and on S
• On the convergence of a novel family of time slicing approximation operators for Feynman path integrals