Posted on Categories:Atomic and Molecular Physics, 原子物理, 物理代写

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 物理代写|原子物理代考Atomic and Molecular Physics代考|Wave–matter duality

It is a matter of common experience that macroscopic physical phenomena reveal either as waves or as particles. By contrast, the Einstein hypothesis about the nature of e.m. waves as a flux of photons challenges this (pre)conception, which we now understand to be only due to the limits of our sensorial experience of the physical word. Light can in fact manifest either as a wave or as a beam of (pseudo)particles, according to the actual phenomenon we are addressing. Certainly the physics of our ocular vision or the propagation of light in vacuum are phenomena very well described by wave equations. On the other hand, the absorption/emission of light by an atomic system or the photoemission of electrons from a metal plate can only be explained by invoking the concept of photon.

In principle, we could speculate that this duality is similarly valid for massive particles, as first discussed by L de Broglie in 1924. If for a photon we can relate wave-like and particle-like properties through such relations as $E=h \nu$ or $\mathbf{p}=\hbar \mathbf{k}$ (where $\mathbf{p}$ is the photon momentum and $\mathbf{k}$ is the wavevector of the corresponding e.m. wave), then we could guess that a matter wave of wavelength $\lambda$ is associated with any particle with mass $m$ and moving with velocity $\mathbf{v}$ according to
$$\lambda=\frac{h}{p}=\frac{h}{m v}=\frac{h}{2 m E_{\text {kin }}}$$
where $\mathbf{p}=m v$ is of course the particle momentum and $E_{\text {kin }}=m v^{2} / 2$ is its kinetic energy. This statement is nothing other than a speculation if no experimental evidence is supplied to support it.

## 物理代写|原子物理代考Atomic and Molecular Physics代考|A constitutive equation for matter waves

Once we acknowledge that any microscopic particle, say an electron, behaves as a matter wave, we must duly feel committed in the search for the constitutive equation ruling over the physics of such unfamiliar waves. This is indeed a very subtle problem that, as a matter of fact, is still an open issue of intense fundamental research. We can nevertheless draw a semi-empirical picture which could be the conceptual guideline in developing a more satisfying formal theory.

As a first step we recognise that any wave, of whichever nature, is described by the d’Alembert equation. Accordingly, if we name $\Psi(x, t)$ the wavefunction of the matter wave describing an electron in one-dimensional motion with speed $v$, we can write
$$\frac{\partial^{2} \Psi(x, t)}{\partial x^{2}}-\frac{1}{v^{2}} \frac{\partial^{2} \Psi(x, t)}{\partial t^{2}}=0$$
where $x$ indicates the direction of motion. By assuming an harmonic time dependence $\Psi(x, t)=\psi(x) \exp (i \omega t)$ we easily get
$$\frac{d^{2} \psi(x)}{d x^{2}}+\left(\frac{\omega}{v}\right)^{2} \psi(x)=0$$
where $\omega=v k=2 \pi v / \lambda$ and $k=2 \pi / \lambda$ is the wavenumber of the matter wave with de Broglie wavelength $\lambda=h / m_{\mathrm{e}} v$. Equation (1.30) is easily rewritten in the more useful form
$$\frac{d^{2} \psi(x)}{d x^{2}}+\left(\frac{m_{\mathrm{e}} v}{\hbar}\right)^{2} \psi(x)=0$$

## 物理代写|原子物理代考Atomic and Molecular Physics代考|Wave-matter duality

$$\lambda=\frac{h}{p}=\frac{h}{m v}=\frac{h}{2 m E_{\text {kin }}}$$

## 物理代写|原子物理代考Atomic and Molecular Physics代考|A constitutive equation for matter waves

$$\frac{\partial^{2} \Psi(x, t)}{\partial x^{2}}-\frac{1}{v^{2}} \frac{\partial^{2} \Psi(x, t)}{\partial t^{2}}=0$$

$$\frac{d^{2} \psi(x)}{d x^{2}}+\left(\frac{\omega}{v}\right)^{2} \psi(x)=0$$

$$\frac{d^{2} \psi(x)}{d x^{2}}+\left(\frac{m_{\mathrm{e}} v}{\hbar}\right)^{2} \psi(x)=0$$

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。