# Quantum Mechanics in Phase Space

@article{Curtright2012QuantumMI, title={Quantum Mechanics in Phase Space}, author={Thomas L. Curtright and C. Zachos}, journal={arXiv: History and Philosophy of Physics}, year={2012}, volume={1}, pages={37-46} }

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 Jose Moyal in the 1940s. While the formalism for quantum mechanics in phase space was wholly cast at that… Expand

#### 136 Citations

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AbstractThe Fermi gF(x,p) function provides a phase space description of quantum mechanics
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In this paper, we show that for a… Expand

States in the Hilbert space formulation and in the phase space formulation of quantum mechanics

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The family of trajectories-based approximations employed in computational quantum physics and chemistry is very diverse. For instance, Bohmian and Heller's frozen Gaussian semiclassical trajectories… Expand

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We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous… Expand

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