  We propose an analytical procedure to fully solve a two-level system coupled
to phonons. Instead of using the common formulation in terms of linear and
quadratic system-phonon couplings, we introduce different phonons depending on
the system electronic level. We use this approach to recover known results for
the linear-coupling limit in a simple way. More importantly, we derive results
for the quadratic coupling induced by a phonon frequency change, a problem
considered up to now as not analytically solvable.
