Abstract: The invariant eigen-operator method is successfully applied to solving energy levels for some quantum systems＇ Hamihonian. For two-dimensional coupled quantum harmonic oscillators, the Hamihonian energylevel gap can be obtained with convenience and directness by this method. Then the Hamiltonian needs not to be diagonalized. The results show that the energy-level gaps are different for different coupled forms of two-dimensional quantum harmonic oscillators.

Key words: invariant eigen- operator, two- dimensional coupled harmonic oscillators, energy eigen- value