Abstract: Hamiltonian of two modes coupled harmonic oscillators is general quadric form of generalized coordinates and momenta. After coordinate transformation, it can be expressed as standard quadric form under new bases. Because canonical commutation relation is satisfied among new coordinates, creation operator and annihilation operator are introduced. Thus, coupling between modes is eliminated and Hamiltonian can be simplified as two mode independent harmonic oscillators, problem is solved. This method can be generalized in solving non- identical n modes coupled harmonic oscillators.

Key words: Hamiltonian, coupling, harmonic oscillator