摘要
当三维各向异性谐振子处在一个任意方向的磁场中后,谐振子之间出现耦合.这些耦合谐振子的海森伯运动方程能够写成类似于薛定谔方程的形式.通过一定的变换可以使海森伯运动方程解耦合,利用这些结果也可以使哈密顿量对角化,进而得到系统的能量本征值和体系的本征态.同时给出了坐标和动量的矩阵元以及量子涨落.
When the three dimensional （3D） anisotropic harmonic oscillators are exposed to a magnetic field, coupling appears among the harmonic oscillators. The Heisenberg equations of motion for these coupled oscillators can be written as the form similar to Shr6dinger equation. Through certain transformations, these Heisenberg equations of motion can be decoupled, and the Hamiltonian can be diagonalized by using these results. Furthermore, the energy eigenvalues and eigenstates of the system are obtained. Meanwhile, the matrix elements of the coordi- nate and momentum are given. The quantum fluctuations are also calculated.
出处
《物理与工程》
2015年第1期39-43,共5页
Physics and Engineering
基金
天津市科委资助项目(11JCYBJC26900)
关键词
量子力学
谐振子
磁场
海森伯运动方程
quantum mechanics
harmonic oscillator
magnetic field
Heisenberg equation of motion
