有限自由度谐振子系统的力学问题

The Mechanics of Finite-Freedom-Degree Harmonic Oscillator System

研究了有限自由度的谐振子系统 ,先给出了它的运动方程 ,并对其求解 ,又导出它的运动方程的拉格朗日形式和哈密顿形式 .将谐振子系统量子化后 ,由海森伯方程也可得出其运动方程 .最后把经典力学和量子力学同时运用到谐振子系统的多种状态并且把它们推广到n维 ,从而验证了海森伯方程和哈密顿正则方程对谐振子系统的等价性 .

Finite freedom degree harmonic oscillator system is studied as follows: To begin with, its equation of motion is given and its solution is obtained by solving the equation, then the Lagrange and Hamiltan equations of motion of harmonic oscillator system are derived from variational principle. Further more, after harmonic oscillator system are quantized, we can also get its motion equation stem from the Heisenbergs Equation. In addition, classical mechanics and quantum mechanics are simultaneously applied to many kinds of conditions (including n dimensional states) of harmonic oscillator systems. Finally, the equivalence of canonical equation and Heisenbergs Equation to harmonic oscillator systems are verified.