摘要
双模耦合谐振子哈密顿量是广义坐标■和广义动量■的一般二次型,通过一个坐标变换可以将其表示为新基底下的标准二次型,经计算得知,新基底之间满足准正则对易关系,从而引入准粒子的产生和湮没算符,这样就消除了耦合项,哈密顿量化简成为双模独立谐振子情形,使问题得到解决.这样的解决方法可以推广到各向异性n模谐振子的耦合体系.
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.
出处
《大学物理》
北大核心
2008年第4期7-9,共3页
College Physics
基金
西安邮电学院中青年教师科研基金资助项目(105-0413)
关键词
哈密顿量
耦合
谐振子
Hamiltonian
coupling
harmonic oscillator