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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/theory-of-angular-momentum
课程评论：没有评论
课程名称：角动量理论 课程概述：本课程可作为学分课程ECEA 5611，属于科罗拉多大学博尔德分校电气工程硕士学位的一部分。课程介绍了量子力学中的角动量算符概念及其与旋转算符的关系，随后呈现角动量算符、其特征值和特征函数，最后讨论角动量的叠加理论。 学习目标： 1. 运用量子力学定义的角动量算符描述和分析角动量态； 2. 解角动量特征值方程； 3. 量子力学地叠加角动量。 课程大纲： 1. **轨道角动量与氢原子**：在本模块中，我们将介绍角动量理论课程，并介绍轨道动量的量子力学定义。接着，我们将使用球面谐波来表达轨道角动量特征态，并用它们来描述氢原子的状态。 2. **旋转与角动量**：在本模块中，我们介绍基于旋转算符的一般角动量算符定义。这个一般定义涵盖了轨道角动量和自旋角动量。随后，我们推导出角动量的最基本性质——其笛卡尔分量之间的对易关系，最后讨论自旋1/2系统的性质。 3. **角动量的一般理论**：该模块涵盖角动量的一般理论。我们从角动量的对易关系开始，定义角动量特征态。接着，使用角动量特征态作为基集构建旋转算符的矩阵表示。最后，我们讨论如何在量子力学中叠加角动量。
Name:Orbital Angular Momentum and Hydrogen Atom
Description:In this module we will introduce the course on the theory of angular momentum and then introduce the quantum mechanical definition of orbital momentum. We will then use the spherical harmonics to express the orbital angular momentum eigenstates and use them to describe the hydrogen atom states.
Name:Rotation and Angular Momentum
Description:In this module, we introduce the general definition of angular momentum operator based on rotation operator. This general definition allows both orbital and spin angular momentum. We then derive the most fundamental property of angular momentum - commutation relations among their Cartesian components. Finally, we discuss the properties of spin-1/2 system.
Name:General Theory of Angular Momentum
Description:This module covers the general theory of angular momentum. We start with the commutation relation of angular momentum and define angular momentum eigenstates. We then construct matrix representation of rotation operators using the angular momentum eigenstates as the basis set. Finally, we discuss how to quantum mechanically add angular momenta.
This course can also be taken for academic credit as ECEA 5611, part of CU Boulder’s Master of Science in Electrical Engineering degree. This course introduces the quantum mechanical concept of angular momentum operator and its relationship with rotation operator. It then presents the angular momentum operators, their eigenvalues and eigenfunctions. Finally, it covers the theory of angular momentum addition. At the end of this course learners will be able to: 1. describe and analyze angular momentum states using quantum mechanically defined angular momentum operators, 2. solve angular momentum eigenvalue equations and 3. add angular momenta quantum mechanically.
