Exact quantum electrodynamical results are obtained for a semiconductor qua
ntum dot placed inside a microcavity of arbitrary photon leakage (kappa), a
nd radiative (gamma) and nonradiative (gamma(c)) decay rates. Analytical re
sults are obtained for the density matrix elements. The absorption spectra
thus obtained for arbitrary values of kappa, gamma and gamma(c) exhibit the
solid-state analogue of the vacuum Rabi splitting when the system decay pa
rameters are much smaller than the quantum dot-cavity-field coupling parame
ter. Numerical estimates are made for samples of CdS and GaAs quantum dots
of dimensions 19 Angstrom and 56 Angstrom, respectively. The results are in
qualitative agreement with the experimental observations.