非线性薛定谔方程经典正则化和正则变换

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=1,…,n-1)和相位差Qα(α=1,…,n-)构成经典哈密顿量的正则变量,而几率差zα=Pα...

CLASSIC REGULARIZATION OF NONLINEAR SCHRODINGER EQUATION AND CANONICAL TRANSFORMATION

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.