Wigner phase space distribution as a wave function

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.

6 pages and 2 figures

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• Study on a Phase Space Representation of Quantum Theory
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• Short-time Fourier transform of the pointwise product of two functions with application to the nonlinear Schrödinger equation
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• Separability and entanglement in classical eigenfunctions as a criterion for Hamiltonian chaos
• Extended Hilbert Phase Space and Dissipative Quantum Systems