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## 物理代写|热力学代写Thermodynamics代考|Can Statistical Mechanics Be Used to Calculate the Properties of Real Fluids?

The idealized systems that have been examined in Question $2.4$ are of immense value as limiting cases approached occasionally by real systems. The analysis presented is necessarily simplified in a number of ways compared to that which needs to be applied to real materials. The majority of the differences between real systems and the idealized models we have considered lie in the fact that the non-interacting particles of the idealized system must be replaced by particles that interact. In the case of molecular entities, they interact through intermolecular forces which can affect the total energy of the ensemble of molecules because the total internal energy is not simply the sum of that of individual molecules. It is this difference which is the subject of this question where we illustrate the use of statistical mechanics for the evaluation of the thermodynamic properties of fluids. We are not attempting to be comprehensive in this question, and the reader is referred to specialized texts for greater detail and breadth (e.g. McQuarrie 2000).

## 物理代写|热力学代写Thermodynamics代考|What Is the Canonical Partition Function?

As has been explained previously, the role of statistical mechanics is that of a bridge between the microscopic and macroscopic descriptions of the system. The statistical mechanics of systems at equilibrium, from which the thermodynamic properties may be obtained, is based upon two postulates. The first postulate, concerning the probability distribution of molecules occupying available energy microstates and how this relates to bulk thermodynamic properties, was introduced earlier in Question 2.1, and has enabled us to evaluate some of the properties of some idealized systems. To try to calculate the properties of more complex systems that are less than ideal in some way, in particular where the molecules interact with each other, we need to move away from the single molecular partition function discussed earlier to the canonical partition function, Q. To introduce this concept, we first consider a real system in a thermodynamic state defined by the macroscopic variables of thermodynamics and consisting of $N$ molecules. The individual molecules in this system are in an unknown quantum state, but we know that a very large number of systems must exist in which individual molecules are in different states, but the overall thermodynamic state is the same. The collection of all of these possible systems is consistent with the real system, each of which is a unique quantum state of the system, called the canonical ensemble.

The second postulate of statistical mechanics states that the only dynamic variable upon which the quantum states of the entire canonical ensemble depend is the total ensemble energy. From this postulate, we deduce that all states of the ensemble having the same energy are equally probable. It can then be shown (Sandler 2010; Reed and Gubbins 1973; Hill 1988) that the probability $\Pi_{i}$ that a system selected at random from the ensemble will be found in quantum state $i$ varies exponentially with the energy $E_{i}$ of that state. That is
$$\Pi_{i}\left(E_{i}\right) \propto \exp \left(-\frac{E_{i}}{k_{\mathrm{B}} T}\right) .$$
Since, however, there is unit probability that the system resides in some state, we have that $\Sigma_{i} \Pi_{i}\left(E_{i}\right)=1$ and
$$\Pi_{i}\left(E_{i}\right)=\frac{\exp \left{-E_{i} /\left(k_{\mathrm{B}} T\right)\right}}{Q},$$
where
$$Q(N, V, T)=\sum_{i} \exp \left(-\frac{E_{i}}{k_{\mathrm{B}} T}\right) .$$

## 物理代写|热力学代写Thermodynamics代考|What Is the Canonical Partition Function?

$$\Pi_{i}\left(E_{i}\right) \propto \exp \left(-\frac{E_{i}}{k_{\mathrm{B}} T}\right) .$$

\left 的分隔符缺失或无法识别

$$Q(N, V, T)=\sum_{i} \exp \left(-\frac{E_{i}}{k_{\mathrm{B}} T}\right)$$

## 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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## 物理代写|电磁学代写Electromagnetism代考|Poisson Bracket Method

In this section we give a detailed treatment of the fields based on the use of the Poisson brackets. The main motivation for the presentation of this method, widely used in classical mechanics, is that it provides the starting point for the quantization of the fields and the quantum theory of radiation.
Consider a set of generalized coordinates $q_{s}$ and momenta $p_{s}$. Let
$$H=H\left(p_{s}, q_{s}, t\right)$$
be the Hamiltonian of the system. A Poisson bracket of two quantities $F$ and $G$ is defined as follows:
$${F, G}=\sum_{s}\left(\frac{\partial F}{\partial p_{s}} \frac{\partial G}{\partial q_{s}}-\frac{\partial F}{\partial q_{s}} \frac{\partial G}{\partial p_{s}}\right)$$
The Poisson brackets have the following properties

(1)
\begin{aligned} &\left{p_{s}, q_{t}\right}=\delta_{s t} \ &\left{p_{s}, p_{t}\right}=\left{q_{s}, q_{t}\right}=0 \end{aligned}
(2)
$$\left{F_{1} F_{2}, G\right}=F_{1}\left{F_{2}, G\right}+F_{2}\left{F_{1}, G\right}$$

## 物理代写|电磁学代写Electromagnetism代考|Hamiltonian of a Closed System

We have discussed until now open systems, covering:
(1) The motion of particles in given fields
(2) The Hamiltonian of the A field.
We want now to write the Hamiltonian that is applicable to be closed system. A closed system is a set of charged particles (generic mass $=m_{s}$, generic charge $=e_{s}$ ) plus the fields that they produce.

We can go from a closed system to an open system under certain circumstances. Consider the closed system $A+B$ in Fig. 11.3. The part $B$ is an open system if we can take into account the presence of $A$ only by means of a field produced by $A$ on $B$; this can be done if the reactions of $B$ on $A$ are negligible.

When we use a power supply to energize a system, we can consider the system “open” if we can disregard its reaction on the power supply. A single atom or a single molecule in the absence of any external field is an example of a closed system.

## 物理代写|电磁学代写Electromagnetism代考|Poisson Bracket Method

$$H=H\left(p_{s}, q_{s}, t\right)$$

$$F, G=\sum_{s}\left(\frac{\partial F}{\partial p_{s}} \frac{\partial G}{\partial q_{s}}-\frac{\partial F}{\partial q_{s}} \frac{\partial G}{\partial p_{s}}\right)$$

(1)
lleft 的分隔符竾失或无法识别
(2)
lleft 的分隔符缺失或无法识别

## 物理代写|电磁学代写Electromagnetism代考|Hamiltonian of a Closed System

(1) 给定场中粒子的运动
(2) $A$ 场的哈密顿量。

## 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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## avatest™帮您通过考试

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## 物理代写|电磁学代写Electromagnetism代考|Angular Distribution of Multipole Radiation

Let us examine the following operator:
$$\mathcal{L}=-i\left(\mathbf{k} \times \frac{\partial}{\partial \mathbf{k}}\right)$$

or
\begin{aligned} \mathcal{L}=&-i\left[\begin{array}{ccc} \hat{\mathbf{i}} & \hat{\mathbf{j}} & \hat{\mathbf{k}} \ k_{x} & k_{y} & k_{z} \ \frac{\partial}{\partial k_{x}} & \frac{\partial}{\partial k_{y}} & \frac{\partial}{\partial k_{z}} \end{array} \mid\right.\ =& \hat{\mathbf{i}}\left[-i\left(k_{y} \frac{\partial}{\partial k_{z}}-k_{z} \frac{\partial}{\partial k_{y}}\right)\right] \ &+\hat{\mathbf{j}}\left[-i\left(k_{z} \frac{\partial}{\partial k_{x}}-k_{x} \frac{\partial}{\partial k_{z}}\right)\right] \ &+\hat{\mathbf{k}}\left[-i\left(k_{x} \frac{\partial}{\partial k_{y}}-k_{y} \frac{\partial}{\partial k_{x}}\right)\right] \end{aligned}
This is the “dimensionless” angular momentum operator, and we know its component in spherical coordinates:
\begin{aligned} &\mathcal{L}{x}=i\left(\sin \phi \frac{\partial}{\partial \theta}+\cot \theta \cos \phi \frac{\partial}{\partial \phi}\right) \ &\mathcal{L}{y}=i\left(-\cos \phi \frac{\partial}{\partial \theta}+\cot \theta \sin \phi \frac{\partial}{\partial \phi}\right) \ &\mathcal{L}_{z}=-i \frac{\partial}{\partial \phi} \end{aligned}

## 物理代写|电磁学代写Electromagnetism代考|Outline of Classical Mechanics

The aim of this chapter is to give the Lagrangian and the Hamiltonian formulations of the following systems:
(1) Charged particles interacting with external fields
(2) Fields and their sources (charges and currents)
(3) Charged particles and their fields, plus their interactions
These systems are discussed separately and independently. Systems 1 and 2 contain both free terms (either free particle or free fields) and interaction terms, the latter being the same in both cases. System 3 is essentially a combination of 1 and 2 , taking into account the fact that the interaction terms have to be included only once.

Before proceeding with the tasks described above, we shall review briefly the Lagrangian and Hamiltonian formulation of classical mechanics.

## 物理代写|电磁学代写Electromagnetism代考|Angular Distribution of Multipole Radiation

$$\mathcal{L}=-i\left(\mathbf{k} \times \frac{\partial}{\partial \mathbf{k}}\right)$$

$$\mathcal{L} x=i\left(\sin \phi \frac{\partial}{\partial \theta}+\cot \theta \cos \phi \frac{\partial}{\partial \phi}\right) \quad \mathcal{L} y=i\left(-\cos \phi \frac{\partial}{\partial \theta}+\cot \theta \sin \phi \frac{\partial}{\partial \phi}\right) \mathcal{L}_{z}=-i \frac{\partial}{\partial \phi}$$

## 物理代写|电磁学代写Electromagnetism代考|Outline of Classical Mechanics

(1) 带电粒子与外场相互作用
(2) 场及其源 (电荷和电流)
(3) 带电粒子及其场，以及它们的相互作用

## 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:Electromagnetism, 物理代写, 电磁学

## 物理代考|电磁学代考Electromagnetism代考|PHYS2213 Complex Field

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## 物理代考|电磁学代考ELECTROMAGNETISM代考|Complex Field

The use of a complex exponential time dependence for the fields is a convenience that may allow us to express Maxwell equations in simple forms. The physically meaningful fields are the real parts of the complex quantities. The notation
$$\mathbf{E}=\mathbf{E}{0} e^{i \omega t}$$ implies that the field is actually given by $$\mathbf{E}=\mathbf{E}{0} \cos \omega t$$

The representation of physical variables by means of complex quantities is based on the understanding that, at the end of the calculations involving these variables, only their real parts will be used. This prescription applies also to the square of a physical variable, for which the meaningful quantity is the square of the real part (which is different from the real part of the square). Therefore, if a field $\mathbf{A}$ is expressed in complex form, in order to obtain the time average of its square value, we have first to find the real part of $\mathbf{A}$, square it, and then average the result over one period. In many cases, such as that of a plane, monochromatic wave, such a calculation is simple. In other circumstances the complex functions are more complicated than $e^{i \omega t}$ and the calculations require more elaborate efforts. However, some useful relations may be found that simplify the task of obtaining the time average of squared monochromatic quantities.

## 物理代考|电磁学代考ELECTROMAGNETISM代考|Electromagnetic Waves in Vacuum and in Continuous Media

The Maxwell equations in the absence of charges and currents $(\rho=j=0)$ become homogeneous equations that may have solutions different from zero. We will not be concerned at this point with the production of electromagnetic waves, but rather with waves that can exist independently from the sources.

The macroscopic Maxwell equations, in the absence of true charges and true currents $\left(\rho_{\text {true }}=\mathbf{j}_{\text {true }}=0\right)$ can be written as follows:
$$\begin{array}{r} \nabla \cdot \mathbf{D}=0 \ \nabla \times \mathbf{E}+\frac{1}{c} \frac{\partial \mathbf{B}}{\partial t}=0 \ \nabla \cdot \mathbf{B}=0 \ \boldsymbol{\nabla} \times \mathbf{H}-\frac{1}{c} \frac{\partial \mathbf{D}}{\partial t}=0 \end{array}$$

## 物理代考|电磁学代考ELECTROMAGNETISM代考|Complex Field

$$\mathbf{E}=\mathbf{E} 0 e^{i \omega t}$$

$$\mathbf{E}=\mathbf{E} 0 \cos \omega t$$

## 物理代考|电磁学代考ELECTROMAGNETISM代 考|Electromagnetic Waves in Vacuum and in Continuous Media

$$\nabla \cdot \mathbf{D}=0 \nabla \times \mathbf{E}+\frac{1}{c} \frac{\partial \mathbf{B}}{\partial t}=0 \nabla \cdot \mathbf{B}=0 \boldsymbol{\nabla} \times \mathbf{H}-\frac{1}{c} \frac{\partial \mathbf{D}}{\partial t}=0$$

## 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。