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

A Study of an N Molecule Quantized-Radiation-Field Hamiltonian