天津职业技术师范大学学报

求解耦合谐振子的薛定谔方程是量子力学的一个重要问题之一。将耦合谐振子的海森堡运动方程写成类似于薛定谔方程的形式,通过一定的变换使其解耦合,进一步使哈密顿量对角化,从而得到薛定谔方程的解。对于磁场中的二维各向异性谐振子,得到了对角化的哈密顿量形式以及能量本征值和体系的本征态。这样的推导过程图像清晰,容易理解。

It is one of the important problems to solve the Schrodinger equation for the coupled harmonic oscillators.Here the Heisenberg equations of motion for the coupled harmonic oscillators are written in the form of Schrodinger type equation,which can be decoupled by certain transformation.Further,the Hamiltonian can be diagonalized.For the anisotropic harmonic oscillator in a background magnetic field,the diagonalization form of the Hamiltonian,the energy eigenvalues and the eigenstates are derived.Such a process of derivation has clear physical picture and is easy to understand.