## 物理代写|理论力学作业代写Theoretical Mechanics代考|Physics2513

2022年7月8日

couryes-lab™ 为您的留学生涯保驾护航 在代写理论力学Theoretical Mechanics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写理论力学Theoretical Mechanics代写方面经验极为丰富，各种代写理论力学Theoretical Mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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
couryes™为您提供可以保分的包课服务

## 物理代写|理论力学作业代写Theoretical Mechanics代考|Classical ensembles with “Uncertainty Principle”

Feynman’s program, however, is still based on the conventional formalism of QM: state vectors in Hilbert space or wave functions in coordinates’ space. In fact, Wigner’s function $W(q, p)$ (pseudoprobability density for sharp values $q, p$ of incompatible variables $q$ and $p$ ) is defined by the expression
$$W(q, p)=\int \text { dy exp }(-i p y) \psi(q+(1 / 2) y) \psi^{*}(q-(1 / 2) y)$$
which contains explicitly the wave function of the state..In Feynman’sapproach waves are therefore still needed to start with, because pseudoprobabilities are first expressed in terms of wave functions, and then forgotten. We will show, however, that it is possible to express Quantum Mechanics from first principles in terms of pseudoprobabilities without ever introducing the concept of probability amplitudes. This program has been recently carried on [Cini 1999] by generalizing the formalism of classical statistical mechanics in phase space with the introduction of two postulates (uncertainty and discreteness), which impose mathematical constraints on the set of quantum variables in terms of which any physical quantity can be expressed. $\mathrm{QM}$ is therefore reformulated in terms of expectation values of quantum variables as a generalization of the correspondent classical varibles of classical statistical mechanics, with the introduction of a single quantum postulate.

This goal will be attained in two steps. The first step is the formulation of a classical Uncertainty Principle. We consider all the classical ensembles of particles in phase space with coordinate $\mathbf{q}$ and momentum $\mathbf{p}$ in which a given variable $\mathbf{A}(\mathbf{q}, \mathbf{p})$ has a well determined value $\alpha$ and its conjugate variable $\mathbf{B}(\mathbf{q}, \mathbf{p})$ is completely undetermined 1 . Only ensembles of this kind in fact are the classical limit of the quantum states.

## 物理代写|理论力学作业代写Theoretical Mechanics代考|The quantum postulate

The second, essential, step is to introduce the quantum into this scheme. This is done by imposing the fulfilment of a second postulate, based on the assumption that the founding stone of quantum theory is the experimental fact that physical quantities exist (the action of periodic motions, the angular momentum, the energy of bound systems..) whose possible values form a discrete set, invariant under canonical transformations, characteristic of each variable in question. This means that we should request that a belongs to a discrete spectrum independent of the phase space variables.

This feature can only be ensured if eq. (8) for the classical characteristic function $\mathrm{Ca}{a}(\mathrm{k}, \mathrm{x})$, which yields a continuous spectrum a for the values of the classical variable $\mathbf{A}$, is modified to become a true Fredholm homogeneous integral equation for the quantum characteristic function $C{i}(k, y)$ with a nonseparable kernel $g(k y-l u x)$, alluwing for the existence of a discrete set of eigenvalues $\alpha_{i}$.
$$\iint \mathrm{dx} d \mathrm{~h} \mathrm{a}(\mathrm{h}-\mathrm{k}, \mathrm{y}-\mathrm{x}) \mathrm{g}(\mathrm{ky}-\mathrm{hx}) C_{\mathrm{i}}(\mathrm{h}, \mathrm{y})=\mathrm{a}{\mathrm{i}} \mathrm{Ci}(\mathrm{k}, \mathrm{y})$$ Similarly, eq.(12) expressing the uncertainty principle between the classical variables $\mathbf{A}$ and $B$ should be changed into $$\iint \mathrm{dy} d h a(h-k, y-x) f(k y-h x) C{i}(h, y)=0$$
for the quantum characteristic function $C_{\mathrm{i}}(\mathrm{k}, \mathrm{x})$ of the ensemble caracterized by one of the values $a_{i}$ of the quantum variable $A$ and by the complete indeterminacy of its quantum conjugate variable $\boldsymbol{B}$. The functions $g()$ and $f()$ should be determined by imposing new self consistent rules for the quantum variables involved.

The two eqs (13) (14), however, cannot be obtained from (7) and (11) as in the classical case by ordinary commuting numbers. In fact the only way to obtain (13) (14) is to replace the classical characteristic variables $C(k, x)$ obeying the standard rule of multiplication of exponentials with quantum variables $C(\mathrm{k}, \mathrm{x})$ having the property
$$\begin{gathered} (1 / 2)[\mathcal{C}(\mathrm{k}, \mathrm{x}) \mathcal{C}(\mathrm{h}, \mathrm{y})+\mathcal{C}(\mathrm{h}, \mathrm{y}) \mathcal{C}(\mathrm{k}, \mathrm{x})]= \ \mathrm{g}(\mathrm{ky}-\mathrm{hx}) \mathcal{C}(\mathrm{k}+\mathrm{h}, \mathrm{x}+\mathrm{y}) \end{gathered}$$
and to replace their classical Poisson bracket with the Quantum Poisson Bracket
$${C(\mathrm{k}, \mathrm{x}), C(\mathrm{~h}, \mathrm{y})}_{\mathrm{QPB}}=\mathrm{f}(\mathrm{ky}-\mathrm{hx}) \mathcal{C}[(\mathrm{k}+\mathrm{h}),(\mathrm{y}+\mathrm{x})]$$

## 物理代写|理论力学作业代写Theoretical Mechanics代考|Classical ensembles with “Uncertainty Principle”

$$W(q, p)=\int \mathrm{dy} \exp (-i p y) \psi(q+(1 / 2) y) \psi^{*}(q-(1 / 2) y)$$

## 物理代写|理论力学作业代写Theoretical Mechanics代考|The quantum postulate

$$\iint \mathrm{dx} d \mathrm{ha}(\mathrm{h}-\mathrm{k}, \mathrm{y}-\mathrm{x}) \mathrm{g}(\mathrm{ky}-\mathrm{hx}) C_{\mathrm{i}}(\mathrm{h}, \mathrm{y})=\mathrm{aiCi}(\mathrm{k}, \mathrm{y})$$

$$\iint \mathrm{dy} d h a(h-k, y-x) f(k y-h x) C i(h, y)=0$$

$$(1 / 2)[\mathcal{C}(\mathrm{k}, \mathrm{x}) \mathcal{C}(\mathrm{h}, \mathrm{y})+\mathcal{C}(\mathrm{h}, \mathrm{y}) \mathcal{C}(\mathrm{k}, \mathrm{x})]=\mathrm{g}(\mathrm{ky}-\mathrm{hx}) \mathcal{C}(\mathrm{k}+\mathrm{h}, \mathrm{x}+\mathrm{y})$$

$$C(\mathrm{k}, \mathrm{x}), C(\mathrm{~h}, \mathrm{y})_{\mathrm{QPB}}=\mathrm{f}(\mathrm{ky}-\mathrm{hx}) \mathcal{C}[(\mathrm{k}+\mathrm{h}),(\mathrm{y}+\mathrm{x})]$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。