Wigner phase-space distribution as a wave function

@article{Bondar2013WignerPD,
  title={Wigner phase-space distribution as a wave function},
  author={Denys I. Bondar and Renan Cabrera and Dmitry V Zhdanov and Herschel A. Rabitz},
  journal={Physical Review A},
  year={2013},
  volume={88},
  pages={263-271}
}
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… 

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