波函数

Utilizing wave function expansion method, all of the potential functions of scattered waves are transformed into one coordinate system with the aid of Graff's addition theorem.

使用波函数展开法，利用一组圆柱坐标系统和Graff加法转换定理，将散射波势函数的表达式变换到同一个坐标系。

The scattering coefficients of a single charged sphere are deduced. And with spherical vector wave functions and addition theorem, the scattering coefficients of multiple charged and uncharged spheres are derived. The sampling method of simulating a Gaussian beam in use of MC is provided.

详细推导了单个带电球粒子的散射系数；并采用矢量波函数展开方法结合矢量波函数的加法定理导出了高斯波束入射多个带电/不带电球粒子的散射系数；提出了用MC模拟高斯波束的抽样方法。

On the basis of the improved averaged atomic model,the distribution of the free electrons is dealt with by the partial-wave method to improve the precision of determination of the energy level,electron populations and atomic inner energy.

在改进的平均原子模型的基础上，在中心场近似下用分波法处理自由电子密度分布函数，提高了电子波函数、电子占据数等原子参数的计算精度。

To explain the time-resolved fluorescence depletion, we develop a dynamics theory of spectroscopy for a vibrational relaxation process, and a decay rate constant of the vibrational state on the excited electronic state is taken to be 〓〓 in which γ is vibrational relaxation rate constant of the transition 0→1 and k〓 is the Boltzmann constant.

电子激发态上的波函数可写作〓相比于以前密度矩阵理论的布居表象，本文所提出的波函数表象理论为在更本质的层次上揭示振动弛豫过程的物理图象，特别是研究超短脉冲激发下含有振动弛豫的动力学光谱创造了条件。

Take the method of "subarea" and "conjunction" to segment the whole request model to three parts. Making use of boundary continuousness between medium and lining structure at stress and displacement, construct a wave function that can satisfy the stress boundary condition at horizontal surface by the scattering of SH-waves in circular part. And then, availing of the wave function, conjoin the circular part into the semi-circular hollow space at common boundary. The problem can be reduced to solve the question that can only meet the condition of "conjunction". Finally, the solution of the problem can be summarized to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite algebraic equations.

采用"分区"与"契合"的方法，将整个求解区域分割成三部分，利用介质与衬砌结构在边界上的应力、位移的连续性，构造一个可以自动满足水平界面上应力边界条件的圆域对SH波散射的波函数；再利用这一波函数将圆域与半圆形凹陷半空间的"公共边界"进行"契合"，将问题简化成对一个只需满足'契合'边界条件的散射问题的求解；最终归结为对一组无穷代数方程组的求解问题，利用截断有限项的方法对其进行计算。

The experimental results show that temperature error and non-linearity of silicon piezoresistive pressure sensor can be reduced markedly.

本文针对其缺点，提出了以正交的局部函数——小波函数作为激励函数的小波神经网络对硅压阻式压力传感器的温度误差进行补偿。

In chapter 4, the Newlands harmonic wavelet is improved and a new type of wavelet with better time-frequency characteristic is constructed. Frequency band of signal can be divided arbitrary with the improved harmonic wavelet so that the phenomena of aliasing are reduced. Several typical fault signals in Electromechanical System are analyzed with it. In addition to the improved harmonic wavelet in chapter 4, a new half-complex wavelet is presented to improve the complex wavelet, which is given by Chaari.O. A unilateral recursive algorithm is derived to improve the real-time characteristic. A parameter n is imported to make the time-frequency and filtering characteristics of it better and its ability of extracting fault feature is enhanced.

第四章通过对Newland谐波小波的改进构造频域紧支撑、时域性能良好的新型小波函数，可实现信号频带的任意划分，从而减少频带混叠现象，采用改进的谐波小波对多种典型的机电系统故障信号进行了分析；以Chaari.O复小波为基础构造了一个半复小波，从提高复小波算法的实时性出发，推导了半复小波单向递推算法，通过给原小波设置可调参数的方法，实现了一种能满足小波基本条件的复值小波，可以通过参数的调整调节小波滤波器在Hilbert空间的时频特性和相应的滤波性能，以加强半复小波对故障特征的提取能力。

In spherical polar coordinates, DRSC potential have supersymmetry and shape invariance for θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrodinger equation with double ring-shaped Coulomb potential are presented. The normalized angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.

本文研究了双环形Coulomb势Schrdinger方程的束缚态精确解，所采用的方法是首先对双环形Coulomb势的Schrdinger方程在球坐标系中进行分离变量，得到相应的角向方程和径向方程；证明双环形Coulomb势在角向和径向具有超对称性和形不变性；根据超对称性和形不变性的性质，获得了角动量量子化条件和束缚态的能谱方程，并将归一化角向波函数用Jacobi多项式表示，将归一化径向波函数用Laguerre多项式函数表示。

The purpose of this study is to present the characteristics of wavelet functions, to compare the effects of choosing different wavelets on wavelet transform, and to discuss the wave shoaling with the help of he WaveletTransform .

本文主旨在於介绍小波函数的特性并探讨不同小波函数对小波转换的影响，再以此分析工具讨论浅化波浪能量於时间－频率域上之变化特性。

In comparison with the drawbacks related to the Fourier Transform and Smoothed Instantaneous Wave Energy History(SIWEH, the Wavelet Transform will be show to be much better suited for analyzing wave shoaling In which signal is believed to be non-stationary and wide band.

在使用小波转换作为分析波浪工具之前，我们选择 Morlet wavelet、Paul wavelet与Gaussian三种型态之小波函数进行讨论，最终考虑视窗面积之大小、复数型态之小波函数及频率视窗的集中度，而以 Morlet wavelet较适合分析波浪。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。