A Study of an N Molecule Quantized-Radiation-Field Hamiltonian
  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. 
Michael Thomas Tavis
quant-ph