通过解这一线性算符的本征值问题，构造一组完备基，并给出完备性和正交性的证明；
We build a set of complete bases through resolving the eigenvalue problem of this linear operator and prove its completeness and orthogonality.
根据电荷算符满足的非线性运动方程，在各单元能量基上，精确地计算了能谱。
By using a nonlinear equation satisfied the charge operator, the spectrum is calculated exactly in energy basis for each cell.
有关算符的统计平均值随时间的演化满足一个封闭的一阶线性微分方程组。
The statistical average values of some relevant operators satisfy a set of differential equations of the first order.
通过引入了一对自共轭算符将涨落项满足的方程线性化，进而得出密度和相涨落所满足的方程。
By introducing a pair of self-conjugate operators, we may linearize the equation of fluctuation term., and get the equations of density and phase fluctuations.
用非线性李代数方法 ，对关于角动量的阶梯算符进行了研究。
Using the method of nonlinear Lie algebra, the tensors of ladder operators are obtained.
本文讨论了线性谐振子的级数解和算符法，导出了两者之间的关系。
The operator theory method lead to the uncertainty relation of one dimensional infinite well;
本文讨论了线性谐振子的级数解和算符法，导出了两者之间的关系。
The operator theory method lead to the uncertainty relation of one dimensional infinite well;
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