Wigner phase-space distribution as a wave function

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

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


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 languageEnglish (US)
Article number052108
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number5
StatePublished - Nov 11 2013

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


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