Solution of the Matrix Hamiltonians via asymptotic iteration method

A method is suggested to obtain solutions of the various quantum optical Hamiltonians in the framework of the asymptotic iteration method. We extend the notion of asymptotic iteration method to solve the 2 \times 2 matrix Hamiltonians. On a particular case, eigenvalues of the Rabi and Rashba Hamiltonians are computed. The method presented here reproduces a number of earlier results in a natural way as well as leads to a novel findings. Possible generalizations of the method are also suggested.