Quantum Mechanics in Phase Space

Details Quantum Mechanics in Phase Space Quantum Mechanics in Phase Space

2011-04-27

arxiv.org/abs/1104.5269v2

Physics

History and Philosophy of Physics

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

Scientific paper

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 Jos\'e 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.

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