非线性薛定谔方程经典正则化和正则变换  

CLASSIC REGULARIZATION OF NONLINEAR SCHRODINGER EQUATION AND CANONICAL TRANSFORMATION

作　　者：夏秀文[1] 罗小兵[1] 陈明伦[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3期32-35,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(2010GQW0033;2009GZW0012)

摘　　要：引入广义坐标和广义动量,可以把量子系统严格地表述为经典哈密顿系统,本文证明了经典哈密顿量中与相位有关的变量可以自然地表述为相位差,因而经典哈密顿量可以实现去约束正则化。对于去约束正则化,证实了波函数(n-1)个分量的几率pα(α=1,…,n-1)和相位差Qα(α=1,…,n-1)构成经典哈密顿量的正则变量,而几率差zα=pα-pn(α=1,…,n-1)和相位差Qα(α=1,…,n-1)不构成经典哈密顿量的正则变量。对于2维量子系统,若保持与相位有关的变换不变,则独立变量((pα-pn)/2,Qα)(α=1,n=2)为经典哈密顿量的一组正则变量。It is well known that quantum system can be translated to classic Hamilton system strictly. We have proven that phase variables of classic Hamiltonian can be described as the form of phase difference variables because quantum system is of gauge transformation. Using these independent variables of （pa,Qa） （a=1,… ,n-1） where pa is the probability amplitude of ath component of wave function and Qa is the phase difference between ath and nth component. Schrodinger equations can be described as Hamilton equations. Furthermore,it has been determined that the variables of probability amplitude and phase difference between ath and nth component are not canonical variables. For two dimension quantum system,as the transformation of phase difference unchanged,it can be tested that the couples variable （（pa-pn）/2,Qa） （a=1,n=2） are another canonical variable.

关 键 词：非线性薛定谔方程 正则变换 哈密顿量 

分 类 号：O413.1[理学—理论物理]