  This paper reexamines the results of Cummings in which the quantum mechanical
two-level-system (TLS) interacts with the electromagnetic field with various
initial distributions and extends that work for both resonant and non-resonant
to times large enough to display multiple photon echoes. The results presented
here include the initial pure coherent state, the field whose initial density
matrix is the Gaussian superposition of coherent states (blackbody radiation)
and density matrices of the field represented by various combinations of mixed
coherent and thermal states with and without squeezing This paper provides, in
addition to the matrix elements to the various states, both the algebraic and
graphical representation for the first order correlation function G=<E+E-> for
resonance and non-resonance. It is found that in all case, the application of
non-resonance leads to oscillations in the first order correlation which was
thought only to apply for the coherent state even for the case of the pure
thermal state.
