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所在平台: Udemy |
课程主页: https://www.udemy.com/course/math-intuition-for-quantum-mechanics-quantum-field-theory/
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**课程名称：** 量子力学与量子场论的数学直觉 **课程概述：** 本课程旨在从数学角度深入讲解量子力学（QM）和量子场论（QFT）的核心概念和方程。课程分为两大部分：第一部分聚焦量子力学的重要概念和方程，第二部分则探讨量子场论。 **先修知识要求：** 鉴于量子力学和量子场论的理论深度和数学复杂度，学生需要具备以下基础知识： 1. **傅里叶级数与傅里叶变换** 2. **多变量微积分** 3. **概率论与随机变量** 4. **经典物理学** 5. **复变函数微积分**（尤其是留数定理和复变积分）——此项主要针对QFT部分 6. **狭义相对论与张量**——用于QFT部分 **重要提示：** * **注意1：** 如果您只对课程的第一部分——量子力学感兴趣，前几项先修知识可能就足够了。本课程内容丰富，总时长达数十小时，您可以选择性地学习您感兴趣的部分。 * **注意2：** 教师非常乐意回答学生关于课程的疑问、提供必要的澄清，或接受任何改进课程质量的建议。 * **注意3：** 教师将持续编辑视频，例如添加笔记，以确保视频讲座清晰易懂。 **部分参考书目（QFT）：** * Quantum Field Theory, M.Srednicki * Quantum Field Theory, Itzykson & Zuber * QFT by Mandl & Shaw * QFT in a nutshell, A.Zee * QFT by Ryder, Ramand * The Quantum Theory of Fields, S.Weinberg * Gauge Theories in Particle Physics, Aitchison & Z.Hey **部分参考书目（QM）：** * Quantum Mechanics: Non-Relativistic Theory, L.D. Landau, E.M. Lifshitz * Principles of Quantum Mechanics, P.A.M. Dirac * Introduction to Quantum Mechanics, David J. Griffiths * Modern Quantum Mechanics, J. J. Sakurai, Jim Napolitano
This course aims to mathematically motivate both Quantum Mechanics (QM) and Quantum field Theory (QFT). The first part is devoted to the most important concepts and equations of QM, whereas the second part deals with QFT. Due to the conceptual and mathematical difficulty of these subjects, some prerequisites to this course are unavoidably required. The student should be familiar with:1) the Fourier Series and Transform;2) Multivariable Calculus;3) Probability theory and random variables;4) Classical Physics;5) Complex Calculus (especially residues and calculation of integrals on a contour), although this is necessary only for some parts of the course devoted to QFT;6) Special Relativity and tensors for QFT.Note 1: the first few prerequisites might be enough if you are interested only in the first part of the course, which is related to QM (consider that this course has tens of hours' worth of material, you might be interested only in some parts);Note 2: I'm more than willing to reply if you have doubts/need clarifications, or -why not- have any recommendations to improve the quality of the course.Note 3: I will still continue to edit the videos (for example by adding notes) to make the video-lectures as clear as possible. Some references for the part on QFT are the following:- Quantum Field Theory, M.Srednicki- Quantum Field Theory, Itzykson & Zuber- QFT by Mandl & Shaw- QFT in a nutshell, A.Zee- QFT by Ryder, Ramand- The Quantum Theory of Fields, S.Weinberg- Gauge Theories in Particle Physics, Aitchison & Z.HeySome references for the part on QM:- Quantum Mechanics: Non-Relativistic Theory, L.D. Landau, E.M. Lifshitz- Principles of Quantum Mechanics, P.A.M. Dirac- Introduction to Quantum Mechanics, David J. Griffiths- Modern Quantum Mechanics, J. J. Sakurai, Jim Napolitano
