Wigner Function

The Wigner function has been studied for more than eight decades. Historically, it was developed from the Schrodinger wave equation, although it could have been developed on its own right. The use of the Wigner function is particularly important in scattering problems and clearly shows the transition to the classical world. In general, the Wigner function is not a positive definite function. One of the interesting aspects of the Wigner function is the ability to transfer many of the results of classical transport theory into quantum approaches merely by replacing the Boltzmann distribution with the Wigner function. The Wigner function for either of the two oscillators can be found by integrating out the coordinates of the other oscillator. Modern approaches with the Wigner function provide a distinct formulation that is recognized as equivalent to, but is a different alternative to normal operator-based quantum mechanics.