  The eigenvalues of the Liouvillians of Markovian master equation for a
harmonic oscillator have a generic form. The Liouvillians considered are
quadratic in the position coordinates or creation and annihilation operators,
as well as having positive renormalized frequencies. We prove this by showing
that a generic Liouvillian of this form can be similarly related to the
Liouvillian of the Kossakowski--Lindblad equation, whose eigenvalues are
already known. The left and right eigenfunctions of the generic Liouvillian
also form a complete and biorthogonal set. Examples of similarly related right
eigenfunctions are given.
