### 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.

Original language | English (US) |
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Article number | 052108 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 88 |

Issue number | 5 |

DOIs | |

State | Published - Nov 11 2013 |

### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics

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## Cite this

Bondar, D. I., Cabrera, R., Zhdanov, D. V., & Rabitz, H. A. (2013). Wigner phase-space distribution as a wave function.

*Physical Review A - Atomic, Molecular, and Optical Physics*,*88*(5), [052108]. https://doi.org/10.1103/PhysRevA.88.052108