Classical Limit
The Wigner function allows one to study the classical limit, offering a comparison of the dynamics in classical and quantum phase space.
It has recently been suggested that the Wigner function approach can be viewed as a quantum analogy to the operatorial formulation of classical mechanics introduced in 1932 by Bernard Koopman and John von Neumann: the time evolution of the Wigner function approaches, in the limit → 0, the time evolution of the Koopman–von Neumann wavefunction of a classical particle.
Read more about this topic: Wigner Quasiprobability Distribution
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