A realization of representation theory

Just when quantum mechanics was created, Dirac discussed the representation theory for it, and later it evidenced the introduction of representations based on Fock states, coherent states, etc. A good representation should provide a complete set of orthonormal basis functions, which allows for an analytical solution of the problem, or the easy attainment of numerical approximation, but it is, however, usually unrealizable. The normalized coherent states we achieved before meet the requirements upon a good representation, in fact, they even provide infinite possibilities for setting up a complete set of orthonormal basis functions since it contains free parameters, thus allowing for choosing alternative representations in due course of attacking a problem, which in turn significantly reduces the computational demands. The first ten energy levels for the Rabi model in the near resonance configuration, with different coupling strengths, were calculated and brought into comparison with that for JC model, the results, as anticipated, confirmed the effectiveness of our method.