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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/foundations-quantum-mechanics
课程评论：没有评论
课程名称：量子力学基础 课程概述：本课程也可作为学术学分修读，作为CU Boulder电气工程硕士学位的ECEA 5610课程。课程涵盖量子力学的基本概念和主题，包括基本概念、一维势阱问题、量子态的时间演化以及基本线性代数。课程提供本科阶段的基础知识，并在此基础上深入更高级的话题。 课程学习目标： 1. 能够全面理解量子力学的基本概念，包括波粒二象性、算符、波函数以及量子态的演变； 2. 掌握量子力学所需的数学工具； 3. 具备学习更高级量子力学及其应用的基础知识。 课程大纲： 1. **波粒二象性与薛定谔方程**：介绍课程及工程师量子力学专门化，讨论波粒二象性和时间独立薛定谔方程，着重于一维无限势阱问题、特征解的性质及希尔伯特空间。 2. **一维势阱问题**：解决多个一维势阱问题，包括有限势阱、谐振子、势垒和势梯问题，讨论解的物理意义以及这些问题表现出的非经典行为。 3. **算符与测量1**：介绍量子力学中的测量理论，从施特恩-盖拉赫实验开始，探讨经典解释的困难，并发展必要的数学工具以正确描述实验结果。 4. **算符与测量2**：扩展前一模块的讨论，介绍哈密顿量、位置和动量算符及它们之间的不确定性关系，同时讨论基变换的一般原则及位置和动量表象的特例。 5. **量子态的时间演变**：讨论如何描述量子系统的时间演变，介绍薛定谔和海森堡两种等价方法，通过时间相关的薛定谔方程和海森堡运动方程来获得时间演化，具体实例讲解谐振子并引入粒子流。 6. **集合体与相同粒子**：处理集体的问题，首先讨论纯态与混合态之间的区别，以及如何使用密度矩阵描述它们，接着探讨不可区分粒子及交换作用，最终进入热分布函数的讨论。
Name:Wave-particle Duality and Schrödinger Equation
Description:In this module we will introduce the course and the Quantum Mechanics for Engineers specialization. In addition, we will discuss wave-particle duality, time-independent Schrödinger equation. one-dimensional infinite potential well problem, properties of eigensolutions and Hilbert space.
Name:One-dimensional Potential Problems
Description:In this module, we will solve several one-dimensional potential problems. They include finite potential well, harmonic oscillator, potential step and potential barrier. We will discuss the physical meaning of the solutions and highlight any non-classical behaviors these problems exhibit.
Name:Operators and Measurements 1
Description:This module covers the theory of measurements in quantum mechanics. We start our discussion by introducing Stern-Gerlach experiment and the difficulty in interpreting the results classically. We then develop mathematical tools required to properly describe the results and then apply them to the interpretation of Stern-Gerlach experiments.
Name:Operators and Measurements 2
Description:In this module we expand upon the discussion from the previous module and introduces Hamiltonian, position and momentum operators and the uncertainty principle that governs the relationship between the operators. We also discuss the general principle of change of basis and the specific example of position and momentum representations.
Name:Time Evolution of Quantum States
Description:This module discusses how to describe the time-evolution of a quantum system. There are two equivalent methods, Schrödinger and Heisenberg pictures, where the time evolution can be obtained by the time-dependent Schrödinger equation and Heisenberg equation of motion, respectively. We will discuss the specific example of harmonic oscillator and finally introduce the particle current.
Name:Ensembles and Identical Particles
Description:This module discusses how to deal with ensembles. We will first discuss the difference between pure and mixed states and how to use the density matrix to describes them. We then discuss indistinguishable particles and exchange interaction, which eventually lead us to the thermal distribution functions.
This course can also be taken for academic credit as ECEA 5610, part of CU Boulder’s Master of Science in Electrical Engineering degree. This course covers the fundamental concepts and topics of quantum mechanics which include basic concepts, 1D potential problems, time evolution of quantum states, and essential linear algebra. It provides undergraduate level foundational knowledge and build on them more advanced topics. At the end of this course learners will be able to: 1. demonstrate full grasp of basic concepts in quantum mechanics including wave-particle duality, operators and wavefunctions, and evolution of quantum states, 2. achieve mastery of the mathematical apparatus needed for quantum mechanics and 3. attain foundational knowledge required to learn more advanced quantum mechanics and applications.
