Quantum mechanics of two modes two photons coupled oscillators

A quantum mechanical model of two modes two photons coupled oscillators is considered. The wave functions is both number state (Schrödinger picture) and coherent state are obtained. By constructing the Dirac operators accurately, the Hamiltonian model is diagonalized. The Heisenberg equations of motion are solved, and discussion related to the squeezing phenomena is given. The Greenʹs function and the average value of the energy are calculated; the transition amplitude between the coherent states in absence and presence of the self-coupling parameters as well as the eigenstates are given