| 有限自由度谐振子系统的力学问题 |
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| 引用本文： | 李惠玲,田俊龙.有限自由度谐振子系统的力学问题[J].山西师范大学学报,2003,17(1):28-37. |
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| 作者姓名： | 李惠玲 田俊龙 |
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| 作者单位： | [1]山西师范大学物理与信息工程学院，山西临汾041004 [2]山西师范大学现代物理研究所，山西临汾041004 |
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| 基金项目： | 山西省回国留学人员科研基金和山西省自然科学基金资助项目 . |
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| 摘 要： | 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，又导出了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。
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| 关 键 词： | 有限自由度 谐振子系统 完整系 量子力学 运动规律 哈密顿形式 |
| 文章编号： | 1009-4490(2003)01-0028-10 |
| 修稿时间： | 2002年8月12日 |
The Mechanics of Finite-Freedom-Degree Harmonic Oscillator System |
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| LI Hui ling,TIAN Jun long.The Mechanics of Finite-Freedom-Degree Harmonic Oscillator System[J].Journal of Shanxi Teachers University,2003,17(1):28-37. |
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| Authors: | LI Hui ling TIAN Jun long |
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| Abstract: | 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. |
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| Keywords: | Harmonic oscillator Degree of freedom Holonomic system |
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