  We study the dispersion properties of electron plasma waves, or plasmons,
which can be excited in quantum plasmas in the nonlinear regime. In order to
describe nonlinear electron response to finite amplitude plasmons, we apply the
Volkov approach to non-relativistic electrons. For that purpose, we use the
Schr\"odinger equation and describe the electron population of a quantum plasma
as a mixture of quantum states. Within the kinetic framework that we are able
to derive from the Volkov solutions, we discuss the role of the wave amplitude
on the nonlinear plasma response. Finally, we focus on the quantum properties
of nonlinear Landau damping and study the contributions of multi-plasmon
absorption and emission processes.
