# Chapter 5: The Wigner Representation

Given a wavepacket, we define the Wigner distribution function,

as: Defining new coordinates we note that

In words, the Wigner distribution function is constructed by first, forming the product of and then Fourier transforming along the difference coordinate, The Wigner distribution is a quasi-probability function for the wavefunction in phase space.

as: Defining new coordinates we note that

In words, the Wigner distribution function is constructed by first, forming the product of and then Fourier transforming along the difference coordinate, The Wigner distribution is a quasi-probability function for the wavefunction in phase space.

- Evolution of the Wigner distribution for a particle in half a box
- Wigner distribution of a coherent state and squeezed states in a harmonic potential
- Wigner distribution of a coherent state in an anharmonic potential
- Wigner distribution of a collision of a Gaussian with an Eckart barrier
- Wigner distribution of a vibrational wavepacket in I
_{2}produced by chirped excitation