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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|高能物理代写High Energy Physics代考|Compton Scattering

The study of the properties of light described in Chap. 1 saw important development in the early 20 th century with the study of X-rays discovered by Röntgen in 1895 . Their name already indicated a total ignorance of their true nature, but it soon became clear that they were actually highly energetic photons. The work of Barkla, Von Laue, and Bragg had shown that the X-rays are scattered in matter, but contrary to the prediction of classical Electromagnetism, their frequency also changes (besides their being deviated from the direction of the original beam). In 1923, Compton published a study in which he attributed a momentum to the quanta of light (photons) as if they were material particles, in total harmony with Einstein’s initial ideas. Thus, the collision of a photon with an electron, impossible in classical theory, gained reality in the new Quantum Pysics initiated by Max Planck [4]. In Compton’s work, the hypothesis of the momentum of the photon was consistent with (but not inspired by) the ideas of Einstein and Planck, and he proceeded to demonstrate that the frequency of the initial radiation would have to change when it collided with the electrons of a gas, using only the conservation of the momentum and the energy in the collision, as schematized in Fig. 2.2.

Since the Compton process must satisfy conservation of energy and of the two components of the momentum of Fig. 2.2, we obtain the following three conditions:
$$\begin{gathered} m_{\mathrm{e}} c^2+h v=E^{\prime}+h v^{\prime} \ \frac{h v}{c}=\frac{h v^{\prime}}{c} \cos \theta+m_{\mathrm{e}} \gamma \mathbf{v} \cos \phi \ \frac{h v^{\prime}}{c} \sin \theta-m_{\mathrm{e}} \gamma \mathbf{v} \sin \phi=0 \end{gathered}$$
This is a system of algebraic equations that can be solved to find $v, v^{\prime}, \theta$, and $\phi$. After some algebraic manipulations and setting $\lambda=c / v$, we have
$$\frac{c}{h}=\frac{1}{v^{\prime}}-\frac{1}{v} \longrightarrow \lambda-\lambda^{\prime}=2 \lambda_{\mathrm{C}} \sin ^2 \frac{\theta}{2},$$
where the quantity $\lambda_{\mathrm{C}}=h / m_{\mathrm{e}} c$ is the Compton wavelength of the electron. Numerically, $\lambda_{\mathrm{C}} \approx 2.4 \times 10^{-4} \AA$ is a very small number, and so the change in the frequency of light is also small. However, it is clear that $\lambda-\lambda^{\prime}>0$ and the photons lose energy which was transferred to the electrons in the scattering process, thus known as inelastic scattering.

## 物理代写|高能物理代写High Energy Physics代考|Pair Production

As discussed in Chap. 1, the formulation of Quantum Physics significantly changed our notion of the vacuum and established that this is the state of minimum energy, but not really a “vacuum” in any classical sense, since there are permanent fluctuations and an energy density is attributable to it. A relationship between energy and mass (probably the most famous formula in the world) was obtained by Einstein in his Special Theory of Relativity:

$$E=m c^2,$$
a relation which, together with the idea of antiparticles in the quantum realm, led to the following concept. Consider a (real) photon with high enough energy $E$. Equation (2.12) would allow this photon to give rise spontaneously to a particle-antiparticle pair by converting its energy into the pair’s mass. Such a process is illustrated in Fig. $2.5$.

If $\omega$ is the frequency of the photon and $\gamma=1 / \sqrt{1-(v / c)^2}$ is the Lorentz factor, we can immediately write down the conservation of energy and momentum at the vertex:
$$\begin{gathered} \hbar \omega=2 \gamma m_{\mathrm{e}} c^2, \ 2 \gamma m_{\mathrm{e}} v=\frac{\hbar \omega}{c} \frac{v}{c} \end{gathered}$$
As the initial momentum of the photon is $\hbar \omega / c$, and (obviously) $v<c$, it is impossible to satisfy both conditions at once. Thus, the conversion of a photon into a pair cannot happen. In order to satisfy the conservation laws what is needed is (1) a second photon annihilating itself with the first one in the initial state (which is possible but requires a radiation field with an enormous density) or (2) another agent that plays the role of absorbing the additional momentum (usually a nucleus, Fig. 2.6).

In the presence of a $Z$-charged nucleus, we can consider the limit of low energies by comparing the photon energy (in units of the energy of an electron with zero momentum) with a dimensionless quantity related to the Coulomb energy. The “low” energies are those that satisfy the condition $\hbar \omega / m_{\mathrm{e}} c^2 \ll 1 / \alpha Z^{1 / 3}$, or physically those where the photon has enough energy to create the pair, but not enough to trigger more complex effects related to the Coulomb field.

# 贝叶斯网络代考

## 物理代写|高能物理代写高能物理代考|康普顿散射

$$\begin{gathered} m_{\mathrm{e}} c^2+h v=E^{\prime}+h v^{\prime} \ \frac{h v}{c}=\frac{h v^{\prime}}{c} \cos \theta+m_{\mathrm{e}} \gamma \mathbf{v} \cos \phi \ \frac{h v^{\prime}}{c} \sin \theta-m_{\mathrm{e}} \gamma \mathbf{v} \sin \phi=0 \end{gathered}$$

$$\frac{c}{h}=\frac{1}{v^{\prime}}-\frac{1}{v} \longrightarrow \lambda-\lambda^{\prime}=2 \lambda_{\mathrm{C}} \sin ^2 \frac{\theta}{2},$$
，其中数量$\lambda_{\mathrm{C}}=h / m_{\mathrm{e}} c$是电子的康普顿波长。从数字上讲，$\lambda_{\mathrm{C}} \approx 2.4 \times 10^{-4} \AA$是一个非常小的数字，因此光的频率变化也很小。但是很明显，$\lambda-\lambda^{\prime}>0$，光子在散射过程中损失了转移给电子的能量，因此称为非弹性散射

## 物理代写|高能物理代写High Energy Physics代考|配对生成

$$E=m c^2,$$

$$\begin{gathered} \hbar \omega=2 \gamma m_{\mathrm{e}} c^2, \ 2 \gamma m_{\mathrm{e}} v=\frac{\hbar \omega}{c} \frac{v}{c} \end{gathered}$$

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## 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。

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