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.

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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.

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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.

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