  We extend the generating function technique for calculation of single
molecule photon emission statistics [Y. Zheng and F. L. H. Brown, Phys. Rev.
Lett., 90,238305 (2003)] to systems governed by multi-level quantum dynamics.
This opens up the possibility to study phenomena that are outside the realm of
purely stochastic and mixed quantum-stochastic models. In particular, the
present methodology allows for calculation of photon statistics that are
spectrally resolved and subject to quantum coherence. Several model
calculations illustrate the generality of the technique and highlight
quantitative and qualitative differences between quantum mechanical models and
related stochastic approximations. Calculations suggest that studying photon
statistics as a function of photon frequency has the potential to reveal more
about system dynamics than the usual broadband detection schemes.
