  In this dissertation a simple Hamiltonian for a system of inter-acting
molecules and radiation field is developed from a model of N Two-Level
Molecules interacting, via a dipole approximation, with a single mode,
quantized radiation field. The exact eigenvalues and eigenvectors of this
Hamiltonian are compared with analytical results obtained from several
different approximation schemes applied to the simple model. The consequence of
this comparison is the development of validity criteria for the utilization of
these approximation schemes to more difficult problems. For example, an
analysis done here indicates that using an independent molecule approximation
in an explanation of the "build up" of coherent radiation in a gas laser
(maser) may be inappropriate.
