不含时哈密顿线性正则变换和非线性正则变换  

TIME-INDEPENDENT HAMILTON LINEAR AND NONLINEAR CANONICAL TRANSFORMATION

作　　者：张新琴[1] 伍冬兰[1] 陈明伦[1] 罗小兵[1] 

机构地区：[1]井冈山大学数理学院,江西吉安343009

出　　处：《井冈山大学学报（自然科学版）》2011年第4期34-37,共4页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(10965001);江西省自然科学基金项目(2009GZW0012;2010GQW0031);江西省教学改革项目(JXJG-09-15-16)

摘　　要：为解决哈密顿正则变换和循环变量问题,本文研究了不含时线性和非线性正则变换。研究发现从严格意义上讲,不含时正则变换得到的新哈密顿量与变换前的哈密顿量之间可以相差一个任意的、只依赖于时间的函数。文章从线性正则变换出发,给出了不同于利用生成函数作正则变换的条件;对于不含时线性正则变换和非线性正则变换,通过引入变换矩阵M,发现正则变换必须满足|M|=1。利用线性正则变换,可以把不同的哈密顿系统相互联系,对于理解广义坐标和广义动量非常有帮助;利用非线性正则变换,可以构造循环变量,求解哈密顿方程。n order to solve Hamilton canonical transformation and seek cyclic coordinate,we introduce the linear and nonlinear canonical transformation.The results show that the new Hamiltonian after transformation is different strictly from the initial Hamiltonian by an addition of arbitrary function only of time.Due to the additional arbitrary function is nothing to do with Hamilton canonical equation,one can let the function to be zero.Thus the Hamiltonian remains unchanged in time-independent canonical transformation.For the time-independent linear canonical transformation,we introduce a transformation matrix M and prove the determinant of the matrix must equal to 1.It is almost impossible to get a cyclic coordinate by linear canonical transformation.For the time-independent nonlinear canonical transformation,different transformation matrix M has been introduced and proved that its determinant must equal to 1.One can always find a suitable nonlinear canonical transformation to produce a cyclic coordinate.

关 键 词：正则变换 线性变换 非线性变换 循环变量 

分 类 号：O316[理学—一般力学与力学基础]