本征函数

略低于居里点时系统磁化的空间分布可用相应的本征函数描写；

The space varia-tion of magnetization just below the Curie point is described by the corresponding eigenfunction ;

本征函数法和格林函数法是求解数学物理定解问题的常用方法，这些方法要求问题具有齐次线性边界条件。

Eigenfunction and Green ′ s function are the main methods to get the definite solutions of Mathematical physics problems , but the problem should have linear homogeneous conditions .

用本征函数法求苯分子（C6H6）的对称化波函数

Deriving Symmetrized Wave Function of Benzene ( C_6H_6 ) by Eigenfunction Method

Bénard系统的稳定性与本征函数的正交性

The Stability of B é nard System and the Orthogonality of Eigenfunction

本征函数的宇称可以这样确定：当r用－r代替时看波函数的变化。

The parity of the eigenfunction is found by determining what happens to the wave function when r is replaced by - r.

由于对E≥0得到连续的而非分立的允许值，正能量的本征函数叫做连续谱本征函数。

Since we get continuous rather than discrete allowed values for E ≥ 0 , the positive-energy eigenfunctions are called continuum eigenfunction .

K在群上函数空间的本征函数就是群G不可约矩阵元的复共轭。

The eigenfunctions of CSCO & ⅲ in the space of functions on the group are the complex conjugate of the IR matrix elements of group G.

用级数展开，再进行Laplace逆变换，得到其本征函数。

And then to get the required eigenfunctions by apply the expansions of series and inverse Laplace transform .

推广的Black-scholes模型的本征函数解法

Eigenfunction method for a generalization of Black-Scholes

Riesz半群母元广义本征函数系统的完整性

The Completeness of Generalised Eigenfunction of a Class of Infinitesimal Generators of Riesz Semigroups

本文所得Fourier空间中的本征函数形式很简单，可为进一步研究不稳定腔提供一个简便的出发点。

The form of eigenfunctions obtained in the Fourier space are very simple , this result might be used as a convenient start point for further investigation of the unstable optical resonator .

我们讨论了系统的指数镇定及闭环系统的广义本征函数生成Riesz基和谱确定增长条件。

The Riesz basis property , spectrum-determined growth condition and exponential stability for the closed-loop system are concluded .

本文根据平面电路理论，采用Green函数本征函数展开法与多模传输矩阵技术，对介质谐振器型带通滤波器进行了机助优化设计，并且试制了样品，其实验值与计算结果吻合良好。

The eigenfunction expansion of Green 's function and the transmission matrix technique are employed for the computer-aided optimum design of bandpass filters with dielectric resonators based on the planar circuit theory The computed results are in good agreements with the experimental ones .

双电子组态本征函数的3j符号解法

3j symbol 's solution of proper funtions for the two-electron configuration

给出了用格林函数表示的普遍解和相应的Sturm-Liouville本征函数及本征值。

A Green function expression and an equivalent generalized Fourier expansion with corresponding Sturm Liouville eigenfunctions and eigenvalues are given .

对于确定的轨道角动量状态，找到了一组完备且独立的角动量本征函数基，它们是坐标分量的齐次多项式，且满足Laplace方程。

For given orbital angular momentum states , we discover a complete set of independent base-functions , which are homogeneous polynomials in the components of the coordinate vectors and satisfy the Laplace equation .

利用本征函数法（EFM方法）计算了O1h结构磁空间群第一布里渊区部分点的C&G系数。

By eigenfunction method , the authors calculate the C-G coefficients of the structure O 1 h Magnetism Space Group in this paper .

本文利用磁群共表示理论构造出磁空间群的不可约表示，进而利用本征函数法计算了O10h结构磁空间群的CG系数。

In this paper , we calculate the irreducible representation of magnetic space group by using the co-representation theory of magnetic group and calculate the C-G coefficients of the structure for magnetic space group by eigenfunction method ( EFM ) .

讨论了一个在边界上有剪力反馈控制的Euler-Bernoulli梁方程，证明了其广义本征函数生成的根子空间在能量Hilbert空间中是完备的。

A differential operator arisen from an Euler-Bernoulli beam equation under boundary shear force feedback control is studied . It is shown that the root subspace of the system operator is complete in the energy Hilbert space .

远场解由Boussinesq方程制约，用差分方法数值地求解；内场解则从Laplace方程着手，对矩形柱体，分区域按本征函数的展开来表示；

For the outer region , 1-D Boussinesq equations are solved numerically by means of the finite difference method , while the eigenfunction expansion technique is used to solve the Laplace equation in the inner region for a rectangular cylinder .

本文利用本征函数展开法推导了无辐射介质（NRD）波导中的并矢格林函数，给出了其中电型并矢格林函数的完备形式。

In this paper , The dyadic Green 's function for nonradiative dielectric ( NRD ) waveguide is derived by the eigenfunction expansion method . The complete electric dyadic Green 's function for this guide is given .

本文以3j符号为工具求双电子Russell&Saunders耦合本征函数，所得计算公式既可直接用于非等效电子，也可用于等效电子。

The proper funtions for the two-electron configuration of Russell-Saunders cupling had teen found with 3j symbol in this paper . The formula can treat directly the nonequivalent electrons , and treat the equivalent electrons also .

本文导出了介质覆盖直角劈标量柱面波的本征函数解，并采用修正的最陡下降法，导得其远区场解的近似式。其GTD式简洁，便于计算。

The eigenfunction solution of scalar cylindrical wave by a wedge with dielectric coating is obtained , and by taking the modified method of steepest descent , a Far-Zone approximate solution is given , it 's expressed in simple GTD form , and easy to compute .

运用一个包含Wave-CISK机制的斜压半地转8层模式和本征函数展开方法，研究了三种不同的对流凝结加热廓线对低纬大气的30~60天低频振荡的影响。

Based on a baroclinic semi-geostrophic model including Wave-CISK , we discuss the influences of different vertical distribution of heating profiles on 30 ~ 60-day low-frequency oscillation ( LFO ) in the tropics , with a 8-layer dynamic model and eigenfunction method .

本文利用陈金全创立的本征函数法，计算了一些高温超导材料所属的A-15结构空间群在第一布里渊区内的C-G系数。并对计算方法进行了讨论。

In this paper , the eigenfunction method established by Chen Jin-quan is used to compute the Clebsch-Gorden coefficients in regard to coupling between the partial symmetry points and lines with each other in the first Brillouin zone of the structure A-15 space groups .

PDE-GP模型根据波动方程推导出的基函数组是波动过程的本征函数，与外界扰动无关，体现了波动特性和变量间的联系。

Independent of the external interference , the basis functions of the PDE-GP model are the intrinsic functions of the wave equation . The physical correlation of the process variables are presented by the basis functions and incorporated into the PDE-GP model .

本征函数展开绝热消去方法的新应用

New Application of the Method of Adiabatic Elimination by Eigenfunction Expansion

人口算子广义本征函数的非基性质（Ⅱ）

Non & basis property of generalized eigenfunctions of population operattor (ⅱ)

关于人口算子广义本征函数是否构成基的问题

On problem of whether generalized eigenfunctions of population operator constitute a basis

均匀波导管横截面上矢量本征函数的完备性

Completeness of Vector Eigen Functions at the Cross Section of Uniform Waveguide