We examine here several methods for calculating the photon absorption spectrum in a system consisting of an electron coupled to a large number of heavy particles. Past work has shown that calculations of the absorption cross section which treat the heavy particles classically and the electron quantum mechanically lead to qualitative errors. It has been suggested that a Gaussian wave packet description of the nuclear motion will remove these qualitative errors; moreover it will give accurate results in the case when the system has many "heavy" degrees of freedom or the spectrum is taken with low frequency resolution. Here we examine several implementations of this suggestion and show that it fails if a time-dependent Hartree method is used for computing the dynamics but it works very well if one treats the electron motion adiabatically or one uses the time-dependent Hartree equations with an adiabatic initial electronic state. Both methods lead to very efficient computational schemes in which the electronic wave function is calculated once, at one nuclear configuration, per time step.