  The eigenfunctions and eigenvalues of the Fokker-Planck operator with linear
drift and constant diffusion are required for expanding time-dependent
solutions and for evaluating our recent perturbation expansion for probability
densities governed by a nonlinear master equation. Although well-known in one
dimension, for multiple dimensions the eigenfunctions are not explicitly given
in the literature. We develop raising and lowering operators for the
Fokker-Planck (FP) operator and its adjoint, and use them to obtain expressions
for the corresponding eigenvalues and eigenfunctions. We show that the
eigenfunctions for the forward and adjoint FP operators form a bi-orthogonal
set, and that the eigenfunctions reduce to sums of products of Hermite
functions in a particular coordinate system.
