关键词: 耦合系数, 非对易参数, 二模谐振子能谱, 能级差

Abstract: By calculating the Hamiltonian spectra of harmonic oscillators of five kinds： non-coupling reso- nance, non-coupling and coordinate coupling composed resonance, non-coupling and momentum coupling reso- nance, non-coupling and coordinate momentum crossed coupling resonance. Based on the analysis comparison, we have found the following results： first, for the existence of energy level difference which contained non-commuta- tion parameters, when non-commutation parameters are equal to zero, energy level difference which calculated is similar to energy level difference of harmonic oscillators for non coupling resonance, so as to demonstrate the validi- ty of the results ; second it shows that the coupling coefficient of coordinates, the coupling coefficient of momentum and the coefficient of compressibility are influence to energy level difference of harmonic oscillators ; third, for coor- dinate momentum crossed coupling resonance, coupling coefficient of coordinate and momentum which crossed has no effect on energy level difference of harmonic oscillators. A variety of coupled harmonic oscillator spectrum are calculated, the research is wide and comprehensive analysis.

Key words: coupling coefficient, non-commutation parameters, two-mold oscillator energy spectrum, energylevel difference