  Starting from the Wigner-Moyal equation coupled to Poisson's equation, a
simplified set of equations describing nonlinear Landau damping of Langmuir
waves is derived. This system is studied numerically, with a particular focus
on the transition from the classical to the quantum regime. In the quantum
regime several new features are found. This includes a quantum modified bounce
frequency, and the discovery that bounce-like amplitude oscillations can take
place even in the absence of trapped particles. The implications of our results
are discussed.
