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Wigner phase-space distribution as a wave function

Author(s): Bondar, Denys I.; Cabrera, Renan; Zhdanov, Dmitry V.; Rabitz, Herschel A.

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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.
Publication Date: 11-Nov-2013
Citation: Bondar, Denys I., Cabrera, Renan, Zhdanov, Dmitry V., Rabitz, Herschel A. (2013). Wigner phase-space distribution as a wave function. PHYSICAL REVIEW A, 88 (10.1103/PhysRevA.88.052108
DOI: doi:10.1103/PhysRevA.88.052108
ISSN: 1050-2947
EISSN: 1094-1622
Pages: 052108-1 - 052108-6
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW A
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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