  The Tavis-Cummings model (the Dicke model treated in the rotating wave
approximation) describing many two-level systems coupled to a single bosonic
mode, has been long known to show collective semiclassical oscillations when
prepared in an inverted state, with all two-level systems excited, and the
bosonic mode empty. This paper discusses how the quantum dynamics approaches
this semiclassical result for large numbers of two-level systems, focussing on
how the eigenvalues approach their semiclassical limit. The approach to the
semiclassical result is found to be slow, scaling like a power of the logarithm
of the system size. Considering also the effect of weak detuning between the
two-level system and the bosonic field, quantum corrections are again found to
decay slowly with system size, such that for a fixed detuning, the quantum
effects of detuning are greater than the classical effect.
