  We present a closed-form analytical solution to the eigenvalue problem of the
Liouville operator generating the dissipative dynamics of the standard
optomechanical system. The corresponding Lindblad master equation describes the
dynamics of a single-mode field inside an optical cavity coupled by radiation
pressure to its moving mirror. The optical field and the mirror are in contact
with separate environments, which are assumed at zero and finite temperature,
respectively. The optomechanical damping basis refers to the exact set of
eigenvectors of the generator that, together with the exact eigenvalues, are
explicitly derived. Both the weak- and the strong-coupling regime, which
includes combined decay mechanisms, are solved in this work.
