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所在平台: Udemy |
课程主页: https://www.udemy.com/course/relativistic-quantum-mechanics-spin-dirac-equation/
课程评论：没有评论
**课程名称：** 相对论量子力学：自旋与狄拉克方程 **课程概述：** 本课程深入探讨相对论量子力学领域，重点关注自旋和狄拉克方程。作者创建此课程的初衷源于对该主题的热情，并为了避免在现有量子力学及量子场论课程中增加过多内容，从而保持内容的清晰和专注。本课程独立于之前的课程，涵盖了不同的主题。 课程从角动量（特别是内禀角动量）的对易关系出发，逐步引出自旋的概念。因此，建议学习者具备操作符、对易子以及它们与同时测量物理量的关系等方面的先修知识。 在对角动量进行详细阐述后，课程将利用这些概念构建狄拉克方程，并展示自旋如何自然地融入相对论理论。 一旦掌握了狄拉克方程，课程将着手求解自由粒子的狄拉克方程，并推导出守恒量，如哈密顿量和流。 最后，通过推导其他对易关系，课程将得出相对论情境下氢原子的能谱，并与非相对论解进行比较。 **先修要求：** * 操作符（Operators） * 对易子（Commutators） * 对易子与同时测量两个物理量的关系
This is a course on Relativistic Quantum Mechanics. Why did I create this new course even if there is already a course on Quantum Mechanics and Quantum Field Theory? The answer is simple: the main reason is that I am passionate about these topics, but another reason is the fact that my previous course on QM and QFT already contained roughly 40 hours of content, so it would have been too "chaotic" if I added another 10 hours of content.Besides, this course is developed on its own (even if we do not start from scratch). In fact, the topics covered here are not covered in the other course. Here we start from some commutation relations regarding angular momentum, from which we derive the concept of spin. It is therefore recommended to have a prerequisite knowledge of operators and commutators, and how the latter are related to the possibility of measuring two physical quantities simultaneously.After a first part on angular momentum (in particular, intrinsic angular momentum), we use the concepts therein developed to construct the Dirac equation. We will see that the concept of spin is naturally incorporated into the relativistic theory.Once we have the Dirac equation, we will start solving it in the case of a free particle, and we also derive conserved quantities from it (the Hamiltonian, current, etc.).From other commutation relations that we derive, we finally find the spectrum of the hydrogen atom in the relativistic case, and compare it with the non-relativistic solution.
