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Using a concise approach with undetermined coefficients, instead of the conventional diagonalization method, we obtain rigorously the energies and analytical wave functions of the ground state and excited states of a polariton model. The results indicate that our method is not only equivalent to the conventional one, but also has its own advantage. We also study several interesting properties of the polariton ground state.published_or_final_versio

Exact analytical solution of a polariton model: Undetermined coefficient approach