Abstract:

In non-commutative phase space，energy spectrum of three-mode coordinate-momentum coupling harmonic oscillator is analyzed by using the invariant eigen-operator method. The explicit expressions for two kinds of three - mode harmonic oscillators： no coupling and coordinate - momentum coupling are obtained. Some expressions λ0，1 and λ1，1 have be connected with non-commutative parameters θ and φ，others λ0，2 and λ1，2 do not.It is discussed about theeffect of coupling parameters on energy spectrum of three-mode coordinate-momentum coupling harmonic oscillator.The results show that the coupling parameters κ and η have the similar effect on the λ1，1 .Furthermore，they do not have any effect on the λ1，1 when κ and η are equal.

Key words: invariant eigen-operator method, non-commutative phase space, harmonic oscillator ')">coordinate-momentum coupling harmonic oscillator