Posted on Categories:Quantum mechanics, 物理代写, 量子力学

# 物理代写|量子力学代写Quantum mechanics代考|PX3511 The Action of Operators on Bras

avatest™

## 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|量子力学代写Quantum mechanics代考|The Action of Operators on Bras

The operators we have introduced begin life as operators that act on kets, mapping them into other kets; but the definition of these operators is easily extended to allow them to act on bras, whereupon they produce other bras. If $\langle\psi|$ is a bra and $A$ an operator, we denote the action of $A$ on $\langle\psi|$ by $\langle\psi| A$, with the bra to the left. That is, we think of $A$ as acting on kets to the right, but on bras to the left. The definition of $\langle\psi| A$ is as follows. Since $\langle\psi| A$ is supposed to be a new bra, it is specified by its action on an arbitrary ket, say, $|\phi\rangle$; the definition is given by writing
$$(\langle\psi| A)(|\phi\rangle)=\langle\psi|(A|\phi\rangle) .$$
Since by this definition the ordering of the parentheses is immaterial, it is customary to drop them, and to write simply
$$(\langle\psi| A)(|\phi\rangle)=\langle\psi|A| \phi\rangle .$$
Thus, we can think of $A$ as acting either to the left or the right in the “matrix element” $\langle\psi|A| \phi\rangle$.

## 物理代写|量子力学代写Quantum mechanics代考|The Outer Product

If $|\alpha\rangle$ and $|\beta\rangle$ are kets, then we can define a linear operator denoted by $|\alpha\rangle\langle\beta|$, whose action on an arbitrary ket $|\psi\rangle$ is given by
$$(|\alpha\rangle\langle\beta|)|\psi\rangle=|\alpha\rangle\langle\beta \mid \psi\rangle,$$

where the right-hand side is the product of the complex number $\langle\beta \mid \psi\rangle$ times the ket $|\alpha\rangle$. The action of $|\alpha\rangle\langle\beta|$ on bras is given by
$$\langle\psi|(|\alpha\rangle\langle\beta|)=\langle\psi \mid \alpha\rangle\langle\beta| .$$
This is not the definition of $|\alpha\rangle\langle\beta|$, which is given by Eq. (47), rather it is a simple consequence of that definition. Its proof will be left as an exercise. The operator $|\alpha\rangle\langle\beta|$ can be viewed as the tensor product of the ket $|\alpha\rangle$ with the bra $\langle\beta|$; this kind of product is similar to the dyadic product used in ordinary vector or tensor analysis. The operator $|\alpha\rangle\langle\beta|$ is called the outer product of $|\alpha\rangle$ and $|\beta\rangle$.

## 物理代写量子力学代写Quantum mechanics代考|The Action of Operators onBras

$$(\langle\psi| A)(|\phi\rangle)=\langle\psi|(A|\phi\rangle) .$$

$$(\langle\psi| A)(|\phi\rangle)=\langle\psi|A| \phi\rangle .$$

## 物理代写|量子力学代写Quantum mechanics代考|The Outer Product

$$(|\alpha\rangle\langle\beta|)|\psi\rangle=|\alpha\rangle\langle\beta \mid \psi\rangle,$$

$$\langle\psi|(|\alpha\rangle\langle\beta|)=\langle\psi \mid \alpha\rangle\langle\beta| .$$

$|\alpha\rangle$ 带着胸置 $\langle\beta|$; 这种乘积类似于荁通向量或张量分析中使用的二进乘积。运荣商 $|\alpha\rangle\langle\beta|$ 称为外积 $|\alpha\rangle$ 和 $|\beta\rangle$.

## 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。