二模谐振子能谱研究

Investigate on Hamiltonian spectrum for two coupled harmonic oscillators

通过对非耦合谐振子系统能谱、非耦合与坐标耦合共同组成的谐振子系统能谱、非耦合与动量耦合共同组成的谐振子系统能谱、非耦合与坐标动量交叉耦合共同组成的谐振子系统能谱和非耦合与压缩项耦合共同组成的谐振子系统5种谐振子能谱进行求解时,通过分析比较发现:其一,对存在非对易参数的能级差的解时,当非对易参数为零时,所求的哈密顿量能级差的解与非耦合谐振子能谱能级差的解相似,从而验证了求解结果的正确性;其二表明了坐标耦合系数、动量耦合系数和压缩性系数都对共同组成的谐振子系统能谱的能级差产生了影响;其三,对非耦合与坐标动量交叉耦合共同组成的谐振子系统能谱而言,坐标动量交叉耦合系数和非对易参数都没有对交叉耦合谐振子的能级差产生任何影响.对多种耦合系统谐振子能谱进行求解,覆盖面广,分析全面.

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.