查询词典 Laguerre polynomial

The PIB of the cylindrically polarized beam depends on the ratio of the waist width to wavelength, the order of the Laguerre polynomial, and the angle between the electrical vector and the radial direction.

束腰宽度与波长的比值、拉盖尔多项式的阶数、电场矢量与径向之间的夹角都对圆柱偏振光束的桶中功率参数产生了重要的影响。

From the ultrashort pulsed Gaussian beams, based on the properties of Laguerre polynomial, a family of solutions are found in theory, which represents a new family of ultrashort pulsed beams called ultrashort pulsed elegant Laguerre-Gaussian beams.

从超短高斯脉冲光束出发，根据拉盖尔多项式的性质，用理论解析推导的方法，给出了一组新的超短脉冲光束的解析解，称为超短复宗量拉盖尔高斯脉冲光束。

By use of the relationships between the hermite polynomial and the laguerre polynomial, the eigenequations of one-dimensional harmonic oscillator and hydrogen atom are conversed into the same equations in form.

同时本文利用SU(1，1)代数将二维、三维情况下的谐振子同加了反平方势的氢原子分别表示成具有相同形式的两算符下的本征值方程，从而得出

In this paper, the current states of research about the basic theory of harmonic oscillator and hydrogen atom in quantum mechanics are firstly reviewed. On base of it, and the relationships between harmonic oscillator and hydrogen atom in quantum mechanics are studied. By use of the relationships between the hermite polynomial and the laguerre polynomial, the eigenequations of one-dimensional harmonic oscillator and hydrogen atom are conversed into the same equations in form. Therefore the relationships between energy levels and wave functions of one-dimensional harmonic oscillator and hydrogen atom are found. Through the coordinates transform, the relationships between energy levels and wave functions of two-dimensional harmonic oscillator and hydrogen atom are found.

首先综述了谐振子与氢原子的基本理论的研究现状，并在此基础上对谐振子与氢原子的关系展开了研究，通过厄密特方程与拉盖尔方程的相互转化，将一维谐振子与一维氢原子的本征值方程转化为相同形式的方程，从而比较得出它们能量及波函数间的关系，并通过坐标变换将直角坐标系下二维氢原子的本征值方程转化成与曲线坐标系下二维谐振子的本征值方程相同的形式，从而得出二维氢原子与二维谐振子的能量及波函数的关系。

With some modifications of Laplace\'s approximation,we obtain uniform asymp-totic formulas for the Stieltjes-Wigert polynomial,the q~(-1)-Hermite polynomial and the q-Laguerre polynomial.

通过将Laplace逼近方法做一些改进，我们得到一些关于Stieltjes-Wigert多项式，q~(-1)-Hermite多项式和q-Laguerre多项式的一致渐近公式。

They can be used to study SU(1,1)displacednumber states and Laguerre polynomial states.

首次得到SU(1，1)位移算符在不可约表示空间中的矩阵元，这对研究SU(1，1)位移粒子数态以及拉盖尔多项式有重要应用。

Chapter 4In this chapter,we applied the generalized Laguerre polynomial as the basis functions and introduced the linear combination technique into WBEPM theory.He atom ground-state energy is studied by using double generalized Laguerre polynomial.The result obtained from this method is at the same level with the other theoretical methods.

第四章本章用广义拉盖尔函数作为基函数，将线性组合技术引入到WBEPM理论中，对He原子的基态能量做了双广义拉盖尔函数的研究，得到可与现有理论方法相比照的结果。

We also develope the corresponding spherical harmonic-generalized Laguerre polynomial mixed spectral method and apply them successfully to computation of three dimensional problems, exterior problems and nonlinear problems.

在第二章中，我们提出了一类新的广义Laguerre多项式正交逼近，其特点是适用于更多问题并能更好地拟合微分方程真解在无穷远处的性态，从而提高了计算精度。

Within the WBEPM theory,the transition probabilities and oscillator strengths of some heavier and light atoms and ions are investigated.We also used the conceptions of spectrum-level-like series and iso-spectrum-level series to study the energy levels of some atoms.Based on the previous work,we used double generalized Laguerre polynomial to calculate the value for the ground-state energy of He atom.

本论文在郑能武教授提出的最弱受约束电子势模型理论基础之上，对若干较重和轻原子离子的跃迁几率和振子强度作了研究；引入类光谱态能级序列的概念和等光谱态能级序列的概念研究了一些原子离子的能级性质；并在前人工作的基础上用双广义拉盖尔函数对氦原子的基态能量做了计算。

Based on polynomial curve-fitting theory, a Laguerre orthogonal basis feed-forward neural network is constructed.

根据多项式理论，构造了一种以Laguerre正交多项式作为隐层神经元激励函数的前向神经网络模型。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。