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提出了一类新的本征函数。A new kind of eigenfunction is presented.

定态波函数形态特征。Morphology of stationary state eigenfunction.

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根据物理上的理由，我们总是剔除把零作为本征函数。We always reject zero as an eigenfunction on the ground of physics.

本征函数法提供了计算各种有限群特征标的统一方法。Eigenfunction method is applied to all kinds of group and easy to formulate.

波函数按力学量算符的本征函数系展开是量子力学的基本问题之一。The expansion of a wave function, according to eigenfunction series of mechanical quantity operator.

文章结合叠加原理，应用本征函数法研究矩形区域上稳定场问题。The stable field problem is discussed in rectangle area with method, which are eigenfunction and superpositionle.

首先，通过理性分析直接求解出矩形域问题所有的本征值及其本征函数向量。At first, all the eigenvalues and their eigenfunction vectors in rectangular domain are solved directly with rational analyses.

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用基于频域的特征方程方法研究线性中立型时滞系统的渐近稳定性。The asymptotic stability of linear neutral delay systems was studied with an eigenfunction approach based on a frequency domain.

并用超势的特性，得到了N维氢原子的本征函数。Under shape invariance potential condition, The energy eigenvalues and eigenfunction of N-dimensional hydrogen atoms are obtained.

在深入分析参数多项式方法数学原理的基础上，提出了参数分布形状特征式法。Based on the deep analysis of the principle of parametric polynomial method, shape eigenfunction method is presented in this paper.

该模型的建立对进一步分析高速干式滚齿过程中的特征参数、进行切削机理的研究具有重要意义。This model has important meaning in analyzing the eigenfunction of the high-speed dry gear hobbing and studying the cutting mechanism.

本文提出了一种双正交本征函数方法并用于对电磁辐射和散射问题的分析。In this paper, a biorthogonal mode eigenfunction method is presented and applied to the analysis of EM radiation and scattering problems.

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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.

本文利用特征函数方法求解了有界圆柱体在冲击载荷作用下的动应力响应历程和分布规律。This paper solves the histories and distributions of dynamic stresses in finite solid cylinder under shocking load by using eigenfunction method.

本文用谱域法结合本征函数技术分析了波导平面混合结构天线单元。An element with mixture structure of waveguides and planar dielectric layers is analyzed using spectral domain approach and eigenfunction technique.

在实时图像分割的过程中，利用特征函数实现图像坐标集合划分简便快捷。In the process of the real-time image partition, using the eigenfunction to realize the partition of image coordinate set is very convenient and easy.

运用非简并微扰方法，求得运动方程的本征函数、本征值以及自旋波的色散关系。The eigenfunction and eigenvalue of the equation are solved by the non-degenerate perturbation theory, as well as dispersion relations for the spin wave.

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第八章研究1维力学和2维弹性力学问题的特征函数展开解法。In chapter 8 solutions by eigenfunction expansion to 1-dimensional problems of mechanics and 2-dimensional problems of theory of elasticity are researched.

研究了斜向波与无限多开孔沉箱的相互作用。An analytical solution based on eigenfunction and matching method is developed for the interaction of oblique waves with infinite number of perforated caissons.

利用分离变量法及本征函数向量展开等方法，推导出裂纹尖端的应力奇性解的计算公式。The method of separation of variables and the method of eigenfunction expansion are used to derive the calculation equations of stress singularities at crack tip.