Exactly and Quasi-Exactly Solvable two-mode Bosonic Hamiltonians

We develop a method to determine the eigenvalues and eigenfunctions of two-boson Hamiltonians include a wide class of quantum optical models. The quantum Hamiltonians have been transformed in the form of the one variable differential equation and the conditions for its solvability have been discussed. Applicability of the method is demonstrated on some simple physical systems.