  We present a numerical solution of the quantum Lenard-Balescu equation using
a spectral method, namely an expansion in Laguerre polynomials. This method
exactly conserves both particles and energy and facilitates the integration
over the dielectric function. To demonstrate the method, we solve the
equilibration problem for a spatially homogeneous one-component plasma with
various initial conditions. Unlike the more usual Landau/Fokker-Planck system,
this method requires no input Coulomb logarithm; the logarithmic terms in the
collision integral arise naturally from the equation along with the
non-logarithmic order-unity terms. The spectral method can also be used to
solve the Landau equation and a quantum version of the Landau equation in which
the integration over the wavenumber requires only a lower cutoff. We solve
these problems as well and compare them with the full Lenard-Balescu solution
in the weak-coupling limit. Finally, we discuss the possible generalization of
this method to include spatial inhomogeneity and velocity anisotropy.
