  In this paper, we construct corrections to the raising and lowering (i.e.
ladder) operators for a quantum harmonic oscillator subjected to a polynomial
type perturbation of any degree and to any order in perturbation theory. We
apply our formalism to a couple of examples, namely q and p 4 perturbations,
and obtain the explicit form of those operators. We also compute the
expectation values of position and momentum for the above perturbations. This
construction is essential for defining coherent and squeezed states for the
perturbed oscillator. Furthermore, this is the first time that corrections to
ladder operators for a harmonic oscillator with a generic perturbation and to
an arbitrary order of perturbation theory have been constructed.
