Posted on Categories:Nuclear Physics, 核物理, 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|核物理代考Nuclear Physics代写|One-particle states

The nucleon has isospin $1 / 2$. In other words, each of the operators $T_1, T_2$ and $T_3$ which are associated with this particle have eigenvalues $\pm 1 / 2$. The operator $T^2=T_1^2+T_2^2+T_3^2$ is proportional to the identity with eigenvalue $3 / 4$.

The states $|\mathrm{p}\rangle$ and $|\mathrm{n}\rangle$, are, by definition, the eigenstates of the particular operator $T_3$
$$T_3|\mathrm{p}\rangle=(1 / 2)|\mathrm{p}\rangle, \quad T_3|\mathrm{n}\rangle=(-1 / 2)|\mathrm{n}\rangle$$
In actual physics, the operator $T_3$ plays a special role since electric charge is related to $T_3$ by
$$Q=T_3+1 / 2$$
The action of $T_1$ and $T_2$ on these states, with $T_{ \pm}=T_1 \pm T_2$, can be written as
\begin{aligned} T_{+}|\mathrm{p}\rangle=0 & T_{-}|\mathrm{n}\rangle=0 \ T_1|\mathrm{p}\rangle=(1 / 2)|\mathrm{n}\rangle & T_1|\mathrm{n}\rangle=(1 / 2)|\mathrm{p}\rangle \ T_2|\mathrm{p}\rangle=(\mathrm{i} / 2)|\mathrm{n}\rangle & T_2|\mathrm{n}\rangle=(-\mathrm{i} / 2)|\mathrm{p}\rangle . \end{aligned}
An arbitrary nucleon state $|N\rangle$ is written
$$|N\rangle=\alpha|\mathrm{p}\rangle+\beta|\mathrm{n}\rangle \quad|\alpha|^2+|\beta|^2=1$$
We remark that all of this is an abstraction applicable only to a world without electromagnetism. A state such as
$$\frac{1}{\sqrt{2}}\left(\left|T_3=1 / 2\right\rangle+\left|T_3=-1 / 2\right\rangle\right),$$
which is oriented along the direction $T_2$ cannot be observed physically. Since it is a superposition of a proton and a neutron, it is both of charge 0 and 1 ; at the same time it creates and doesn’t create an electrostatic field. As such, it is a superposition of two macroscopically different states, an example of a “Schrödinger cat.”

## 物理代写|核物理代考Nuclear Physics代写|The generalized Pauli principle

The Pauli principle states that two identical fermions must be in an antisymmetric state. If the proton and the neutron were truly identical particles up to the projection of their isospin along the axis $T_3$, a state of several nucleons should be completely antisymmetric under the exchange of all variables, including isospin variables. If we forget about electromagnetic interactions, and assume exact invariance under rotations in isospin space, the Pauli principle is generalized by stating that an $A$-nucleon system is completely antisymmetric under the exchange of space, spin and isospin variables. This assumption does not rest on as firm a foundation as the normal Pauli principle and is only an approximation. However, we can expect that it is a good approximation, up to electromagnetic effects.

The generalized Pauli principle restricts the number of allowed quantum states for a system of nucleons. We shall see below how this determines the allowed states of the deuteron.

# 核物理代写

## 物理代写|核物理代考Nuclear Physics代写|One-particle states

$$T_3|\mathrm{p}\rangle=(1 / 2)|\mathrm{p}\rangle, \quad T_3|\mathrm{n}\rangle=(-1 / 2)|\mathrm{n}\rangle$$

$$Q=T_3+1 / 2$$
$T_1$和$T_2$对这些状态的作用，加上$T_{ \pm}=T_1 \pm T_2$，可以写成
\begin{aligned} T_{+}|\mathrm{p}\rangle=0 & T_{-}|\mathrm{n}\rangle=0 \ T_1|\mathrm{p}\rangle=(1 / 2)|\mathrm{n}\rangle & T_1|\mathrm{n}\rangle=(1 / 2)|\mathrm{p}\rangle \ T_2|\mathrm{p}\rangle=(\mathrm{i} / 2)|\mathrm{n}\rangle & T_2|\mathrm{n}\rangle=(-\mathrm{i} / 2)|\mathrm{p}\rangle . \end{aligned}

$$|N\rangle=\alpha|\mathrm{p}\rangle+\beta|\mathrm{n}\rangle \quad|\alpha|^2+|\beta|^2=1$$

$$\frac{1}{\sqrt{2}}\left(\left|T_3=1 / 2\right\rangle+\left|T_3=-1 / 2\right\rangle\right),$$

## 物理代写|核物理代考Nuclear Physics代写|The generalized Pauli principle

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。

Posted on Categories:Nuclear Physics, 核物理, 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|核物理代考Nuclear Physics代写|Nuclear reactions and decays

Nuclear species can be transformed in a multitude of nuclear reactions. In nuclear reactions involving only strong and electromagnetic interactions, the number of protons and the number of neutrons are conserved separately. An important example is neutron absorption followed by photon emission, the so-called ” $(n, \gamma) “$ reaction:
$$\mathrm{n}(\mathrm{A}, \mathrm{Z}) \rightarrow \gamma(\mathrm{A}+1, \mathrm{Z}) \quad \text { i.e. } \quad(\mathrm{A}, \mathrm{Z})(\mathrm{n}, \gamma)(\mathrm{A}+1, \mathrm{Z})$$
The second form is a standard way of denoting the reaction. Other reactions are ” $(\mathrm{p}, \gamma) “$ reactions
$$\mathrm{p}(\mathrm{A}, \mathrm{Z}) \rightarrow \gamma(\mathrm{A}+1, \mathrm{Z}+1) \text { i.e. }(\mathrm{A}, \mathrm{Z})(\mathrm{p}, \gamma)(\mathrm{A}+1, \mathrm{Z}+1)$$
“( $(\mathrm{n}, \mathrm{p}) “$ reactions
$$\mathrm{n}(\mathrm{A}, \mathrm{Z}) \rightarrow \mathrm{p}(\mathrm{A}, \mathrm{Z}-1) \text { i.e. }(\mathrm{A}, \mathrm{Z})(\mathrm{n}, \mathrm{p})(\mathrm{A}, \mathrm{Z}-1)$$
and ” $(\mathrm{p}, \mathrm{n})$ ” reactions
$$\mathrm{p}(\mathrm{A}, \mathrm{Z}) \rightarrow \mathrm{n}(\mathrm{A}, \mathrm{Z}+1) \quad \text { i.e. } \quad(\mathrm{A}, \mathrm{Z})(\mathrm{p}, \mathrm{n})(\mathrm{A}, \mathrm{Z}+1) \text {. }$$
In all these reactions, the final state nucleus may be produced in an excited state so additional photons are produced in de-excitation.

## 物理代写|核物理代考Nuclear Physics代写|Conservation laws

The investigation of the fundamental constituents of matter and their interactions comes from the experimental and theoretical analysis of reactions. These reactions can be scattering experiments with or without production of particles, and decays of the unstable particles produced in these reactions.

Various fundamental conservation laws govern nuclear reactions. The laws allow the identification of particles, i.e. the determination of their masses, spins, energies, momenta etc.

The most important laws are energy-momentum conservation, angular momentum conservation and electric charge conservation. In nuclear physics, other laws play an important role such as lepton number, baryon number and isospin conservation.

In this book, we shall mainly make use of simple “selection rules” implied by these conservation laws. In this section, we will first discuss the experimental and phenomenological consequences of the most important laws. We will then show how the conservation laws are related to invariance properties of transition operators between initial and final states, or, equivalently, invariance laws of Hamiltonians of the systems under consideration.

# 核物理代写

## 物理代写|核物理代考Nuclear Physics代写|Nuclear reactions and decays

$$\mathrm{n}(\mathrm{A}, \mathrm{Z}) \rightarrow \gamma(\mathrm{A}+1, \mathrm{Z}) \quad \text { i.e. } \quad(\mathrm{A}, \mathrm{Z})(\mathrm{n}, \gamma)(\mathrm{A}+1, \mathrm{Z})$$

$$\mathrm{p}(\mathrm{A}, \mathrm{Z}) \rightarrow \gamma(\mathrm{A}+1, \mathrm{Z}+1) \text { i.e. }(\mathrm{A}, \mathrm{Z})(\mathrm{p}, \gamma)(\mathrm{A}+1, \mathrm{Z}+1)$$
($(\mathrm{n}, \mathrm{p}) “$反应)
$$\mathrm{n}(\mathrm{A}, \mathrm{Z}) \rightarrow \mathrm{p}(\mathrm{A}, \mathrm{Z}-1) \text { i.e. }(\mathrm{A}, \mathrm{Z})(\mathrm{n}, \mathrm{p})(\mathrm{A}, \mathrm{Z}-1)$$

$$\mathrm{p}(\mathrm{A}, \mathrm{Z}) \rightarrow \mathrm{n}(\mathrm{A}, \mathrm{Z}+1) \quad \text { i.e. } \quad(\mathrm{A}, \mathrm{Z})(\mathrm{p}, \mathrm{n})(\mathrm{A}, \mathrm{Z}+1) \text {. }$$

## 物理代写|核物理代考Nuclear Physics代写|Conservation laws

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。

Posted on Categories:Nuclear Physics, 核物理, 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

Quantum effects inside nuclei are fundamental. It is therefore surprising that the volume $\mathcal{V}$ of a nucleus is, to good approximation, proportional to the number of nucleons $A$ with each nucleon occupying a volume of the order of $\mathcal{V}_0=7.2 \mathrm{fm}^3$. In first approximation, stable nuclei are spherical, so a volume $\mathcal{V} \simeq A \mathcal{V}_0$ implies a radius
$$R=r_0 A^{1 / 3} \quad \text { with } \quad r_0=1.2 \mathrm{fm} \quad .$$
We shall see that $r_0$ in (1.9) is the order of magnitude of the range of nuclear forces.

In Chap. 3 we will show how one can determine the spatial distribution of nucleons inside a nucleus by scattering electrons off the nucleus. Electrons can penetrate inside the nucleus so their trajectories are sensitive to the charge distribution. This allows one to reconstruct the proton density, or equivalently the proton probability distribution $\rho_p(r)$. Figure 1.1 shows the charge densities inside various nuclei as functions of the distance to the nuclear center.

We see on this figure that for $A>40$ the charge density, therefore the proton density, is roughly constant inside these nuclei. It is independent of the nucleus under consideration and it is roughly 0.075 protons per $\mathrm{fm}^3$. Assuming the neutron and proton densities are the same, we find a nucleon density inside nuclei of
$$\rho_0 \simeq 0.15 \text { nucleons } \mathrm{fm}^{-3} .$$
If the nucleon density were exactly constant up to a radius $R$ and zero beyond, the radius $R$ would be given by (1.9). Figure 1.1 indicates that the density drops from the above value to zero over a region of thickness $\sim 2 \mathrm{fm}$ about the nominal radius $R$.

## 物理代写|核物理代考Nuclear Physics代写|Binding energies

The saturation phenomenon observed in nuclear radii also appears in nuclear binding energies. The binding energy $B$ of a nucleus is defined as the negative of the difference between the nuclear mass and the sum of the masses of the constituents:
$$B(A, Z)=N m_{\mathrm{n}} c^2+Z m_{\mathrm{p}} c^2-m(A, Z) c^2$$
Note that $B$ is defined as a positive number: $B(A, Z)=-E_B(A, Z)$ where $E_B$ is the usual (negative) binding energy.

The binding energy per nucleon $B / A$ as a function of $A$ is shown in Fig. 1.2. We observe that $B / A$ increases with $A$ in light nuclei, and reaches a broad maximum around $A \simeq 55-60$ in the iron-nickel region. Beyond, it decreases slowly as a function of $A$. This immediately tells us that energy can be released by the “fusion” of light nuclei into heavier ones, or by the “fission” of heavy nuclei into lighter ones.

As for nuclear volumes, it is observed that for stable nuclei which are not too small, say for $A>12$, the binding energy $B$ is in first approximation additive, i.e. proportional to the number of nucleons :
$$B(A, Z) \simeq A \times 8 \mathrm{MeV}$$
or more precisely
$$7.7 \mathrm{MeV}<B(A, Z) / A<8.8 \mathrm{MeV} \quad 12<A<225$$
The numerical value of $\sim 8 \mathrm{MeV}$ per nucleon is worth remembering!
The additivity of binding energies is quite different from what happens in atomic physics where the binding energy of an atom with $Z$ electrons increases as $Z^{7 / 3}$, i.e. $Z^{4 / 3}$ per electron. The nuclear additivity is again a manifestation of the saturation of nuclear forces mentioned above. It is surprising from the quantum mechanical point of view. In fact, since the binding energy arises from the pairwise nucleon-nucleon interactions, one might expect that $B(A, Z) / A$ should increase with the number of nucleon pairs $A(A-1) / 2 .{ }^1$ The additivity confirms that nucleons only interact strongly with their nearest neighbors.

# 核物理代写

$$R=r_0 A^{1 / 3} \quad \text { with } \quad r_0=1.2 \mathrm{fm} \quad .$$

$$\rho_0 \simeq 0.15 \text { nucleons } \mathrm{fm}^{-3} .$$

## 物理代写|核物理代考Nuclear Physics代写|Binding energies

$$B(A, Z)=N m_{\mathrm{n}} c^2+Z m_{\mathrm{p}} c^2-m(A, Z) c^2$$

$$B(A, Z) \simeq A \times 8 \mathrm{MeV}$$

$$7.7 \mathrm{MeV}<B(A, Z) / A<8.8 \mathrm{MeV} \quad 12<A<225$$

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。

Posted on Categories:固体物理, 物理代写

## 物理代写|固体物理代写Solid Physics代考|k · p Theory

avatest固体物理Solid Physics代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。avatest™， 最高质量的固体物理Solid Physics作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此固体物理Solid Physics作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

avatest™ 为您的留学生涯保驾护航 在物理Physics代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的物理Physics代写服务。我们的专家在固体物理Solid Physics代写方面经验极为丰富，各种固体物理Solid Physics相关的作业也就用不着 说。

## 物理代写|固体物理代写SOLID PHYSICS代考|k · p Theory

Another approximation method, which is very useful for understanding interactions between bands, uses a perturbation expansion of a different type. This method takes note of the fact that the critical points of the Brillouin zone have well-defined properties. If the energies at these critical points are known, then we can treat the band energy at a nearby point in the Brillouin zone as the sum of the energy at the critical point plus a small perturbation.
We begin by writing the Schrödinger equation in terms of the Bloch functions,
$$\left(\frac{p^2}{2 m}+U(\vec{r})\right) u_{n \vec{k}}(\vec{r}) e^{i \vec{k} \cdot \vec{r}}=E_n(\vec{k}) u_{n \vec{k}}(\vec{r}) e^{i \vec{k} \cdot \vec{r}},$$

where $\vec{p}=-i \hbar \nabla$. Since the derivative of $e^{i \vec{k} \cdot \vec{r}}$ is known, we can rewrite this as
$$\left(\frac{1}{2 m}|\vec{p}+\hbar \vec{k}|^2+U(\vec{r})\right) u_{n \vec{k}}(\vec{r})=E_n(\vec{k}) u_{n \vec{k}}(\vec{r}) .$$
We can then write this as the sum of three terms,
$$\left(H_0+H_1+H_2\right) u_{n \vec{k}}(\vec{r})=E_n(\vec{k}) u_{n \vec{k}}(\vec{r})$$
where
\begin{aligned} H_0 & =\frac{p^2}{2 m}+U(\vec{r}) \ H_1 & =\frac{\hbar}{m} \vec{k} \cdot \vec{p} \ H_2 & =\frac{\hbar^2 k^2}{2 m} . \end{aligned}

## 物理代写|固体物理代写SOLID PHYSICS代考|Other Methods ofCalculating Band Structure

We have already seen in Section 1.6 that the Bloch states of different bands are orthogonal. Since the core electrons are nearly the same as the atomic states, which have slow variation near the atomic nucleus, this means that the electron wave functions for higher levels will tend to have strong spatial oscillations near a nucleus, so that the overlap integral $\int \psi_n^* \psi_m d^3 r$ will vanish. This leads to problems for numerical calculations.

One way to solve for the higher band states without using rapidly oscillating wave functions is the pseudopotential method. In this method, instead of using just the potential $U(\vec{r})$ of the bare nucleus, a new $U(\vec{r})$ is used which includes the effects of the Coulomb repulsion and Pauli exclusion of the core electrons, to repel the electrons in higher states from the core region.

Using this new $U(\vec{r})$, the upper electron states can be calculated using the nearly free electron approximation; the inner, core electron states are assumed to remain nearly the same as the atomic core states. This strong distinction between the two types of states is one of the major assumptions of this method.

There is no exact way of calculating the potential $U(\vec{r})$; in this method one simply starts with a guess and then improves $U(\vec{r})$ by iteration. This can be done either by comparing the calculated band structure to experimental data or by adjusting $U(\vec{r})$ to give self-consistency. Once the valence electron states are calculated, the local charge density due to these electrons can be calculated, which is proportional to $\rho(\vec{r})=\psi^*(\vec{r}) \psi(\vec{r})$. The Coulomb repulsion from this charge density then gives an adjustment to $U(\vec{r})$. Eventually, the adjusted $U(\vec{r})$ will not change upon iteration, when it is consistent with the charge density of the valence states.

The band structure of silicon in Figure 1.26(a) was calculated using a pseudopotential method. Notice how the bands have the character of nearly free electrons – for example, the lowest energy band is nearly parabolic and the next energy band has a maximum at zone center, as in Figure 1.30. In general, pseudopotential methods give reasonable predictions of many band structure parameters, but still require some experimental input for realistic calculations.

## 物理代写|固体物理代写SOLID PHYSICS代考|k · p Theory

$$\left(\frac{p^2}{2 m}+U(\vec{r})\right) u_{n \vec{k}}(\vec{r}) e^{i \vec{k} \cdot \vec{r}}=E_n(\vec{k}) u_{n \vec{k}}(\vec{r}) e^{i \vec{k} \cdot \vec{r}},$$

$$\left(\frac{1}{2 m}|\vec{p}+\hbar \vec{k}|^2+U(\vec{r})\right) u_{n \vec{k}}(\vec{r})=E_n(\vec{k}) u_{n \vec{k}}(\vec{r}) .$$

$$\left(H_0+H_1+H_2\right) u_{n \vec{k}}(\vec{r})=E_n(\vec{k}) u_{n \vec{k}}(\vec{r})$$

\begin{aligned} H_0 & =\frac{p^2}{2 m}+U(\vec{r}) \ H_1 & =\frac{\hbar}{m} \vec{k} \cdot \vec{p} \ H_2 & =\frac{\hbar^2 k^2}{2 m} . \end{aligned}

## 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。

Posted on Categories:固体物理, 物理代写

## 物理代写|固体物理代写Solid Physics代考|Density ofStatesatCritical Points

avatest固体物理Solid Physics代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。avatest™， 最高质量的固体物理Solid Physics作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此固体物理Solid Physics作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

avatest™ 为您的留学生涯保驾护航 在物理Physics代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的物理Physics代写服务。我们的专家在固体物理Solid Physics代写方面经验极为丰富，各种固体物理Solid Physics相关的作业也就用不着 说。

## 物理代写|固体物理代写SOLID PHYSICS代考|Density ofStatesatCritical Points

As we saw in Section 1.6, $\nabla_{\vec{k}} E$ vanishes at zone center and at the boundaries of the Brillouin zone. This means that the density of states will have special properties at these points. It might seem that the density of states diverges at these points, but this is not always the case. For example, in the case of isotropic bands, the density of states formula (1.8.4) can be simplified to
$$\mathcal{D}(E) d E=\frac{V}{(2 \pi)^3} 4 \pi d E \frac{1}{\left|\nabla_{\vec{k}} E\right|} k^2(E)$$

Since the band at zone center must be at a minimum or maximum, we can expand the energy in powers of $k$ as
$$E(k)=E_0+\left.\frac{1}{2} \frac{\partial^2 E}{\partial k^2}\right|{k=0} k^2+\cdots$$ The leading order of the gradient of $E$ is therefore linear in $k$, which means that the density of states is proportional to $k$, which implies $$\mathcal{D}(E) d E \propto \sqrt{\left(E-E_0\right)} d E$$ The same thing occurs at the critical points on the zone boundaries where $\nabla{\vec{k}} E$ vanishes, discussed in Section 1.6. In general, the band minimum or maximum at the critical point can be expanded in powers of $k$ as
$$E(k)=E_0+\frac{1}{2} \sum_{i, j} \frac{\partial^2 E}{\partial k_i \partial k_j}\left(k_i-k_i^{\mathrm{crit}}\right)\left(k_j-k_j^{\mathrm{crit}}\right)+\cdots$$

## 物理代写|固体物理代写SOLID PHYSICS代考|Disorderand Density ofStates

Density-of-states plots give us a natural way to look at the effect of disorder, that is, what happens to the electron bands when a crystal is not perfectly periodic. As discussed in Section 1.1 , bands and band gaps appear whenever there is overlap of atomic orbitals, regardless of periodicity.

In the long wavelength limit (when the characteristic length of the disorder is much longer than the atomic lattice spacing), we can model disorder as regions with slightly larger or smaller spacing between atoms. We can then approximate the effect of the disorder by recalculating the band energy for a larger or smaller lattice spacing in each region. Larger spacing corresponds to less orbital overlap of adjacent atoms, which means less bonding-antibonding splitting. This corresponds to a smaller band gap; in other words, the upper, antibonding states will have lower energy and the lower, bonding states will have higher energy. This means that in a region of larger lattice spacing, there will be electron states inside the nominal energy gap.

In the absence of any other information, we can assume that the disorder is distributed randomly. In the long wavelength limit, we can view the disordered crystal as a set of perfectly ordered crystals with band gaps that are distributed according to a Gaussian distribution, according to the central limit theorem,
$$P\left(E_g\right)=\frac{1}{\sqrt{2 \pi}(\Delta E)} e^{-\left(E_g(0)-E_g\right)^2 / 2(\Delta E)^2},$$
where $E_g$ is the band gap for a perfectly ordered crystal and $\Delta E_g$ is a characteristic range of energy fluctuations. The total density of states of the crystal will then be given by the convolution of this distribution with the density of states for a periodic structure,
$$\mathcal{D}(E)=\int d E_g \mathcal{D}\left(E-E_g\right) P\left(E_g\right)$$

The effect of the convolution is to smear out the band gaps of a solid. Disorder does not necessarily eliminate the existence of bands and band gaps, however. Figure 1.23(b) illustrates how a small degree of disorder smears the bands, while leaving them still much the same. In general, every real crystal has some degree of band smearing because there is always some degree of disorder.

## 物理代写|固体物理代写SOLID PHYSICS代考|Bloch’sTheorem

$$\psi_{n \vec{k}}(\vec{r}+\vec{R})=\psi_{n \vec{k}}(\vec{r}) e^{i \vec{k} \cdot \vec{R}}$$

\begin{aligned} & \psi_{n \vec{k}}(\vec{r}+\vec{R}) e^{-i \vec{k} \cdot \vec{r}}=\psi_{n \vec{k}}(\vec{r}) e^{i \vec{k} \cdot \vec{R}} e^{-i \vec{k} \cdot \vec{r}} \ & \psi_{n \vec{k}}(\vec{r}+\vec{R}) e^{-i \vec{k} \cdot(\vec{R}+\vec{r})}=\psi_{n \vec{k}}(\vec{r}) e^{-i \vec{k} \cdot \vec{r}} . \end{aligned}

$$\psi_{n \vec{k}}(\vec{r})=\frac{1}{\sqrt{V}} u_{n \vec{k}}(\vec{r}) e^{i \vec{k} \cdot \vec{r}},$$

## 物理代写|固体物理代写SOLID PHYSICS代考|BravaisLattices and ReciprocalSpace

$$\vec{R}=N_1 \vec{a}_1+N_2 \vec{a}_2+N_3 \vec{a}_3$$

## 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。