2012/02/29 by Denys I. Bondar, Renan Cabrera, Dmitry V. Zhdanov +1 · 1 citation
Physics and Astronomy · Mathematics · #quant-ph #math-ph #math.MP #physics.atom-ph
paper · pdf · doi:10.1103/physreva.88.052108
published as Phys. Rev. A 88, 052108 (2013) · 6 pages and 2 figures
arxiv created 2013/11/12 · arxiv updated 2013/11/20
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.