Perturbative calculation of the adiabatic geometric phase and particle in a well with moving walls

We use the Rayleigh-Schrodinger perturbation theory to calculate the correc tions to the adiabatic geometric phase due to a perturbation of the Hamilto nian. We show that these corrections are at least of second order in the pe rturbation parameter. As an application of our general results we address t he problem of the adiabatic,geometric phase for a one-dimensional particle which is confined to an infinite square well with moving walls.