eigenfunction

简明释义

英[/ˈaɪɡənˌfʌŋkʃən/]美[/ˈaɪɡənˌfʌŋkʃən/]

n. [数]特征函数（等于 proper function）

英英释义

单词用法

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例句

1.A 3-d theoretical model of an OWC with a harbour system has been presented, based on the method of eigenfunction, source distribution and matching the inner region with outside.

本文根据特征函数加源分布、内外域拟合的方法，建立了振动水柱港池系统的三维理论模型。

2.This paper solves the histories and distributions of dynamic stresses in finite solid cylinder under shocking load by using eigenfunction method.

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。

3.In 1990s based on the eigenfunction method of representation theory of groups, a new method, the symmetrized boson representation (SBR) method, was brought forward.

90年代，陈金全等人在点群的表示理论上提出了一种新的方法，对称化玻色表象方法(SBR)。

4.Two basic methods of solution of the Fokker-Planck equation, i. e. the method of the representation of eigenfunction and that of the path integral, are discussed.

本文讨论了福克-普朗克方程的两种基本解法，即本征函数展开和路径积分方法。

5.We always reject zero as an eigenfunction on the ground of physics.

根据物理上的理由，我们总是剔除把零作为本征函数。

6.In chapter 8 solutions by eigenfunction expansion to 1-dimensional problems of mechanics and 2-dimensional problems of theory of elasticity are researched.

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。

7.Under shape invariance potential condition, The energy eigenvalues and eigenfunction of N-dimensional hydrogen atoms are obtained.

并用超势的特性，得到了N维氢原子的本征函数。

8.Eigenfunction is used to describe ambiguity sets for analog circuit diagnosis. Fault isolation and conditional fault isolation are proposed to identify isolation ability of test node.

采用故障特征函数描述模拟电路故障字典法中的模糊集，提出了节点故障隔离度和条件故障隔离度的概念，用其描述节点对故障的区分能力。

9.In quantum mechanics, an eigenfunction 特征函数 represents a state of a system with a definite energy level.

在量子力学中，eigenfunction 特征函数 表示具有确定能量水平的系统状态。

10.The Schrödinger equation can be solved by finding the eigenfunctions 特征函数 of the Hamiltonian operator.

通过寻找哈密顿算符的 eigenfunctions 特征函数 可以解决薛定谔方程。

11.In linear algebra, the eigenfunction 特征函数 is associated with a specific eigenvalue.

在线性代数中，eigenfunction 特征函数 与特定的特征值相关联。

12.The eigenfunctions 特征函数 of a differential operator can be used to construct solutions for boundary value problems.

微分算子的 eigenfunctions 特征函数 可用于构造边值问题的解。

13.In signal processing, the Fourier transform can be viewed as finding the eigenfunctions 特征函数 of the time-domain signal.

在信号处理中，傅里叶变换可以视为寻找时域信号的 eigenfunctions 特征函数。

作文

In the realm of mathematics and physics, the term eigenfunction refers to a special type of function that is associated with certain operators. Understanding eigenfunctions is crucial for solving a variety of problems, particularly in quantum mechanics and differential equations. An eigenfunction is defined as a non-zero function that, when acted upon by a linear operator, yields a scalar multiple of itself. This scalar is known as the eigenvalue. The relationship can be expressed mathematically as follows: if L is a linear operator and f is an eigenfunction, then L(f) = λf, where λ is the eigenvalue. The concept of eigenfunctions arises in various fields, most notably in the study of linear differential equations. For example, consider the simple harmonic oscillator in quantum mechanics, where the allowed energy states of the system correspond to specific eigenfunctions. These functions represent the probability distributions of finding a particle in a certain position. The significance of eigenfunctions lies not only in their mathematical properties but also in their physical interpretations. They provide insights into the behavior of systems under various conditions. Moreover, eigenfunctions play a vital role in Fourier analysis. In this context, any periodic function can be expressed as a sum of sine and cosine functions, which are themselves eigenfunctions of the differentiation operator. This decomposition is fundamental in many applications, including signal processing and image analysis. To further illustrate the importance of eigenfunctions, let’s consider the vibrational modes of a guitar string. When a string is plucked, it vibrates in specific patterns, each corresponding to a distinct eigenfunction. These modes determine the sound produced by the string, and each mode has a unique frequency associated with it, which is the eigenvalue. Musicians and acoustics engineers utilize this knowledge to design instruments that produce desired sounds. In summary, the concept of eigenfunctions is a cornerstone in both theoretical and applied mathematics. Their ability to simplify complex problems by breaking them down into manageable components makes them invaluable across various scientific disciplines. By grasping the nature of eigenfunctions, students and professionals alike can unlock deeper understanding and innovative solutions to intricate challenges in their respective fields. As we continue to explore the depths of mathematics and its applications, the significance of eigenfunctions will undoubtedly remain prominent, guiding us toward new discoveries and advancements in technology and science.

在数学和物理领域，术语特征函数指的是与某些算子相关的一种特殊类型的函数。理解特征函数对解决各种问题至关重要，特别是在量子力学和微分方程中。特征函数被定义为在施加于线性算子时，产生自身的标量倍数的非零函数。这个标量称为特征值。这种关系可以用数学表达如下：如果L是一个线性算子，而f是一个特征函数，那么L(f) = λf，其中λ是特征值。 特征函数的概念出现在多个领域，最显著的是在线性微分方程的研究中。例如，考虑量子力学中的简单谐振子，系统的允许能量状态对应于特定的特征函数。这些函数表示在某个位置找到粒子的概率分布。特征函数的重要性不仅在于它们的数学属性，还在于它们的物理解释。它们提供了对系统在各种条件下行为的洞察。 此外，特征函数在傅里叶分析中扮演着至关重要的角色。在这个背景下，任何周期函数都可以表示为正弦和余弦函数的总和，而这些函数本身就是微分算子的特征函数。这种分解在许多应用中是基础，包括信号处理和图像分析。 为了进一步说明特征函数的重要性，考虑吉他弦的振动模式。当弦被拨动时，它以特定的模式振动，每种模式对应于一个独特的特征函数。这些模式决定了弦发出的声音，每种模式都有一个与之相关的独特频率，即特征值。音乐家和声学工程师利用这一知识设计出能够产生所需声音的乐器。 总之，特征函数的概念是理论和应用数学中的基石。它们通过将复杂问题简化为可管理的组件来简化复杂问题，使其在各个科学领域中不可或缺。通过掌握特征函数的性质，学生和专业人士能够解锁更深层次的理解和创新解决方案，以应对各自领域中的复杂挑战。随着我们继续探索数学及其应用的深度，特征函数的重要性无疑将保持突出，引导我们迈向新的发现和科技进步。