Chapter 5: The Wigner Representation

Given a wavepacket, Formul we define the Wigner distribution function,
The Actual Formul as:
The Actual Formul
Defining new coordinates The Actual Formul we note that
The Actual Formul
In words, the Wigner distribution function is constructed by first, forming the product of The Actual Formul and then Fourier transforming along the difference coordinate, The Actual Formul The Wigner distribution is a quasi-probability function for the wavefunction in phase space.