线性谐振子与匀速圆周运动  

Linear Harmonic Oscillator and Uniform Circular Motion

作　　者：岳小萍[1] 秦鑫[1] 

机构地区：[1]新乡医学院生命科学技术系物理教研室,河南新乡453003

出　　处：《新乡学院学报》2012年第4期304-306,共3页Journal of Xinxiang University

摘　　要：用经典力学的方法讨论了质点匀速圆周运动与谐振动的关系问题,给出了线性谐振子位移、速度、加速度表达式,用因果律和牛顿第二运动定律,说明了三者之间的位相差关系;得到了万有引力场中二质点系统线性谐振子力常量k=-Gm1 m2/r3的结果,讨论了其物理意义,纠正了长期以来认为谐振子能量总是大于零的错误认识.引入了线性电谐振子概念;给出了讨论椭圆轨道电线性谐振子、不同轨道上价电子线性电谐振子的方法;介绍了实空间电线性谐振子转化为量子力学线性谐振子的方法.This article discusses the relationship between uniform circular motion and harmonic vibration of particle by classical mechanics method. The expressions of displacement, velocity and acceleration of linear harmonic oscillator are given, and phase differences among the three are explained by causality and Newton＇s second law of motion. This article obtains linear harmonic oscillator force constant k=-Gmlm2/r3 in gravitational field, and discusses its physical significance, corrects the mistake of energy of harmonic oscillator is invariably positive for a long time. Electric linear harmonic oscillator concept is introduced. Method of discussing electric linear harmonic oscilators of elliptic orbit and valence electron in different orbital are provided. The method of converting linear harmonic oscillator of real space to quantum mechanics is introduced.

关 键 词：电线性谐振子 匀速圆周运动 椭圆轨道 谐振动 哈密顿正则方程 正则方法 

分 类 号：O321[理学—一般力学与力学基础] O482.4[理学—力学]