Abstract: By introducing the IEO method and selecting the appropriate invariant eigenoperator, we obtain an invariant eigenoperator function, from which we can derive the corresponding eigenvalue, which is related with the energy level gap of the interesting Hamihonian. Thus we derive the spectrums of this system directly and conveniently. In order to test the present method, we take two examples for a diatomic molecules system with extra field and an optical nonlinear interaction Hamiltonian, and then obtain their corresponding energy level gaps.

Key words: invariant eigenoperator, Sehrodinger equation, Heisenberg equation