Wigner Function's Negativity Demystified

Details Wigner Function's Negativity Demystified Wigner Function's Negativity Demystified

2012-02-16

arxiv.org/abs/1202.3628v1

Physics

Quantum Physics

3 pages, 1 figure

Scientific paper

As early as 1932 Wigner defined the joint distribution for the coordinate and momentum of a quantum particle. Despite a drawback of being sometimes negative, the Wigner distribution has stood the test of time and found many applications. Having demonstrated that the Wigner function of a pure quantum state is a wave function in the specially tuned Dirac bra-ket formalism, we 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. Since probability amplitude need not be positive, our findings elucidate the long-standing mystery of the Wigner function's negativity. 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. As a result, contrary to widespread beliefs, the volume of negative regions in the Wigner distribution cannot quantify the degree of quantum character.

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