Algebraic Bethe anzatz and the Tavis–Cummings model

The $N$-atoms-radiation-field model is solved for its eigenvalues and eigenstates by the Algebraic Bethe anzatz and the comparison with the traditional approach is established. The eigenenergies and the amplitudes of the wave function are expressed through the solutions of the Bethe equations. The determinant representation of the norms of the wave functions and of the expectation values are obtained. The algebraic approach establish the connections of the cinsidered model with the other exactly solvable models.