量子化的

Then the momentum P in the acquired motion equation is replaced by quantum operator, thus we obtain Schrodinger equation for charged particle moving in magnetic fields in Quantum Mechanics. Then we discuss the Gauge transformation and gauge invariance of Schrodinger equation, following which the Dirac phase is introduced.

然后把经典力学中的哈密顿量量子化，得到量子化的带电粒子在磁场中运动的薛定谔方程，之后是薛定谔方程的规范变换和规范不变性，并引入Dirac不可积相因子的概念。

After descibing the concepts, definitionsand operation approaches of quantum group and SLq(2) Lie algebra, the physicalmeaning of quantum group particles is explained in the present thesis. The gaugeinvariance in SLq(2) gauge field and its thermodynamics model is considered basedon the idea of q-deformation. The zero energy gap equation and q-deformed energygap equation are derived under the assumption of q-quantization and semi-classical q-quantization, then the zero-temperature energy gap A(0,q) and crititical temperature〓 can be calculated from the q-energy gap equation.

在介绍了量子群和SLq(2)李代数的基本概念，定义和运算方法后，文中进一步阐述了量子群粒子的物理意义；在q变形思想基础上，本文研究了SLq(2)规范场及其热力学模型中的规范不变性质，并在q量子化和半经典q量子化的假设下导出了零能隙方程和q变形能隙方程；然后从q能隙方程计算了与零温度能隙△(0，q)和临界温度〓。

From the analysis of the spectrum of black-body radiation, the concept of quantization is introduced and the duality of matter and wave is also introduced.

从黑体辐射之频谱分析开始，引入量子化的概念；进而推出物质与波动之二象性。

English Description From the analysis of the spectrum of black-body radiation, the concept of quantization is introduced and the duality of matter and wave is also introduced.

Chinese Description 从黑体辐射之频谱分析开始，引入量子化的概念；进而推出物质与波动之二象性。

In this paper, we research the noncommutative quantum mechanics by deformation quantization.

所以在本文中，我们用变形量子化的方法来研究非对易量子力学。

In terms of the topological invariant in Riemann-Cartan spacetime proposed by Prof. Duan and the φ-mapping topological current theory, we gave the cosmic strings with the complex scalar field and showed that the strings appear in the zeroes of the scalar field. Meanwhile one can find that the length of cosmic strings is quantized in the topological level and the quantum number is determined by Hopf indices and Brouwer degrees.

以段一士教授提出的Riemann-Cartan流形中的新拓扑不变量为基础研究了宇宙弦的拓扑结构，指出宇宙弦只能存在于复标量场的零点处，而且在拓扑层面上是量子化的，而该量子数决定于Hopf指数和Brouwer度。

radiation field ; two-level atom ; quantum bit ; quantum logic gate:unitary transition matrix

近年来，作者研究了量子化的辐射场中的二能级原子的量子相干性

The energy that atoms and molecules can possess according to quantum theory is quantized.

根据量子理论，分子和原子具有的能量是量子化的。

The merits of the inclusion of quantitative methods based on logical empiricism for explicit definition of input errors and uncertainty, approaches to quantisation of input data, and optimisation of outputs are contrasted with soft systems approaches that incorporate more linguistic and information theory into landscape analysis.

为输入的错误和不确定，输入的数据的量子化的方法和输出的最佳化的明白定义以合乎逻辑的经验主义为基础的数量方法的包含的功绩与将较多的语言学和传播理论纳入风景分析的软性系统方法一起对比。

The merits of the inclusion ofquantitativemethods based on logical empiricism for explicit definition ofinput errors and uncertainty , approaches to quantisation ofinputdata , and optimisation of outputs are contrasted with soft systems approaches that incorporate more linguistic and information theory into landscape analysis .

为输入的错误和不确定，输入的数据的量子化的方法和输出的最佳化的明白定义以合乎逻辑的经验主义为基础的数量方法的包含的功绩与将较多的语言学和传播理论纳入风景分析的软性系统方法一起对比。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。