  We present quantum Maxwell-Bloch equations (QMBE) for spatially inhomogeneous
semiconductor laser devices. The QMBE are derived from fully quantum mechanical
operator dynamics describing the interaction of the light field with the
quantum states of the electrons and the holes near the band gap. By taking into
account field-field correlations and field-dipole correlations, the QMBE
include quantum noise effects which cause spontaneous emission and amplified
spontaneous emission. In particular, the source of spontaneous emission is
obtained by factorizing the dipole-dipole correlations into a product of
electron and hole densities. The QMBE are formulated for general devices, for
edge emitting lasers and for vertical cavity surface emitting lasers, providing
a starting point for the detailed analysis of spatial coherence in the near
field and far field patterns of such laser diodes. Analytical expressions are
given for the spectra of gain and spontaneous emission described by the QMBE.
These results are applied to the case of a broad area laser, for which the
frequency and carrier density dependent spontaneous emission factor beta and
the evolution of the far field pattern near threshold are derived.
