  We apply the notion of asymptotic iteration method (AIM) to determine
eigenvalues of the bosonic Hamiltonians that include a wide class of quantum
optical models. We consider solutions of the Hamiltonians, which are even
polynomials of the fourth order with the respect to Boson operators. We also
demonstrate applicability of the method for obtaining eigenvalues of the simple
Lie algebraic structures. Eigenvalues of the multi-boson Hamiltonians have been
obtained by transforming in the form of the single boson Hamiltonian in the
framework of AIM.
