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# 物理代写|量子力学代写Quantum mechanics代考|PHYS402 Compton effect

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## 物理代写|量子力学代写Quantum mechanics代考|Compton effect

The idea that light behaves like particles was strengthened by the analysis of the Compton effect. In this case the experiment involves radiation hitting a metal foil and getting scattered to various angles $\theta$. It turns out that the intensity $I(\lambda)$ of the scattered light (number of scattered photons) plotted against the wavelength $\lambda$ has two peaks: the first is an angle independent peak at a wavelength close to the incident wavelength $\lambda_0$, and the second is another peak at a wavelength which is angle dependent at $\lambda=\lambda_0+\frac{h}{m_e c}(1-\cos \theta)$ (see Fig. $1.3)$

Classical physics applied to this problem fails to explain both the angle and wavelength dependence of the observed phenomena. However, by treating light as a particle, and applying momentum and energy conservation to a billiard ball type scattering, Compton explained the observed phenomena correctly.

Before the collision the photon and electron have relativistic energy-momentum $\left(E_0=h \nu_0, \mathbf{p}0\right)$ and $\left(E{0 e}=m_e c^2, \mathbf{p}_{0 e}=0\right)$ respectively, while after the collision they have $(E=h \nu, \mathbf{p})$ and $\left(E_e=\sqrt{m_e^2 c^4+p_e^2 c^2}, \mathbf{p}_e\right)$ (see Fig. 1.4). Momentum and energy conservation require
\begin{aligned} \mathbf{p}_0 &=\mathbf{p}+\mathbf{p}_e \ h \nu_0+m_e c^2 &=h \nu+\sqrt{m_e^2 c^4+p_e^2 c^2} \end{aligned}

## 物理代写|量子力学代写Quantum mechanics代考|Particle-wave duality

The conclusion from the Planck, Einstein and Compton analyses was that light, which was thought to be a wave classically, could also behave like a particle at the quantum level. It was then natural to ask the question of whether this “particlewave duality” may apply to other objects that carry energy and momentum? For example, could a classical particle such as an electron behave like a wave at the quantum level? Indeed in 1923 DeBroglie postulated such a particle-wave duality and assigned the wavelength
$$\lambda=\frac{h}{p}$$
to any particle that has momentum $p$. This is consistent with the photon’s electromagnetic wave momentum $p=E / c=h \nu / c=h / \lambda$. But he proposed this momentum-wavelength relation to be true for the electron or other classical particles as well, even though the energy-momentum relation for these particles is quite different than the photon’s (i.e. $E=p^2 / 2 m$ or $\left.E=\left(p^2 c^2+m^2 c^4\right)^{1 / 2}\right)$.

## 物理代写|量子力学代写Quantum mechanics代考|Compton effect

$$\mathbf{p}_0=\mathbf{p}+\mathbf{p}_e h \nu_0+m_e c^2 \quad=h \nu+\sqrt{m_e^2 c^4+p_e^2 c^2}$$

## 物理代写|量子力学代写Quantum mechanics代考|Particle-wave duality

“柆子波二象性”是否适用于其他㨹带能量和动量的物体? 例如，电子等经典粒子能否在量子水平上表现得像波? 事实上，德布罗意 在 1923 年假设了这样一种粒子波二象性，并指定了波长
$$\lambda=\frac{h}{p}$$

## 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。