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arXiv · 1202.3628

Wigner phase space distribution as a wave function

Denys I. Bondar·Renan Cabrera·Dmitry V. Zhdanov·Herschel A. Rabitz
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Abstract

We demonstrate that the Wigner function of a pure quantum state is a wave function in a specially tuned Dirac bra-ket formalism and argue that the Wigner function is in fact a probability amplitude for the quantum particle to be at a certain point of the classical phase space. Additionally, we establish that in the classical limit, the Wigner function transforms into a classical Koopman-von Neumann wave function rather than into a classical probability distribution. Since probability amplitude need not be positive, our findings provide an alternative outlook on the Wigner function's negativity.

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Denys I. Bondar, Renan Cabrera, Dmitry V. Zhdanov, Herschel A. Rabitz. 2013-11-12. Wigner phase space distribution as a wave function. https://doi.org/10.1103/physreva.88.052108

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