|
所在平台: Udemy |
课程主页: https://www.udemy.com/course/the-mathematical-beauty-that-led-to-quantum-physics/
课程评论：没有评论
本Coursera课程《统计物理：与量子和热力学的关系》共包含四个部分，深度解析了物理学中两个里程碑式的理论：量子力学和统计力学的奠基。 **第一部分**着重于量子力学的起源，从19世纪末20世纪初的数学发现讲起。课程会详细介绍普朗克的黑体辐射理论，特别是他引入的能量量子化假设，虽然当时被视为数学技巧，却开启了物理学的新纪元。随后，课程将探讨爱因斯坦如何将量子化概念应用于光电效应，提出光子能量量子化的革命性观点。还将了解量子化概念在康普顿效应以及玻尔解释氢原子光谱等关键事件中的应用。课程强调数学工具（如傅里叶级数、帕塞瓦尔定理等）在量子力学发展中的作用，并穿插普朗克解决黑体辐射问题的历史轶事。 **第二部分**深入研究了爱因斯坦1902年关于热平衡和热力学第二定律的开创性工作。课程将解析爱氏论文中使用的数学方法，包括对经典力学基础的填补，以及对热力学第二定律的推广和对熵的力学解释。此外，还将回顾和演示刘维尔定理、哈密顿方程等经典力学概念，这些都是理解爱因斯坦理论的关键。本部分要求学生具备经典物理和相空间的基础知识。 **第三部分**聚焦于爱因斯坦的“奇迹年”（Annus Mirabilis）中的重要论文，特别是对光电效应和布朗运动的解释。课程将深入分析爱因斯坦如何利用统计力学方法解释这些现象，进一步巩固统计物理学的理论基础。 **第四部分**将前面所学知识融会贯通，重点在于利用伊辛模型（Ising model）推导相变（phase transitions）。这一部分将是前面所有知识的实践应用，展示统计物理学在理解宏观物理现象中的强大威力。
First part of the course:The first part of the course showcases the beautiful mathematics that, in the late 19th century/ early 20th century, led to the discovery of a revolutionary branch in physics: Quantum Mechanics. Planck postulated that the energy of oscillators in a black body is quantized. This postulate was introduced by Max Planck in his derivation of his law of black body radiation in 1900. This assumption allowed Planck to derive a formula for the entire spectrum of the radiation emitted by a black body (we will also derive this spectrum in this course). Planck was unable to justify this assumption based on classical physics; he considered quantization as being purely a mathematical trick, rather than (as is now known) a fundamental change in the understanding of the world. In 1905, Albert Einstein adapted the Planck postulate to explain the photoelectric effect, but Einstein proposed that the energy of photons themselves was quantized (with photon energy given by the Planck-Einstein relation), and that quantization was not merely a "mathematical trick". Planck's postulate was further applied to understanding the Compton effect, and was applied by Niels Bohr to explain the emission spectrum of the hydrogen atom and derive the correct value of the Rydberg constant.In addition to the very useful mathematical tools that will be presented and discussed thoroughly, the students have the opportunity to learn about the historical aspects of how Planck tackled the blackbody problem.Calculus and multivariable Calculus are a prerequisite to the course; other important mathematical tools (such as: Fourier Series, Perseval's theorem, binomial coefficients, etc.) will be recalled, with emphasis being put on mathematical and physical insights rather than abstract rigor.Second part of the courseBy the end of June 1902, just after being accepted as Technical Assistant at the Federal Patent Office in Bern, Albert Einstein, 23, sent to the renowned journal Annalen der Physik a manuscript with the bold title "Kinetic Theory of Thermal Equilibrium and of the Second Law of Thermodynamics". In the introduction, he explains that he wishes to fill a gap in the foundations of the general theory of heat, "for one has not yet succeeded in deriving the laws of thermal equilibrium and the second law of thermodynamics using only the equations of mechanics and the probability calculus". He also announces "an extension of the second law that is of importance for the application of thermodynamics". Finally, he will provide "the mathematical expression of the entropy from the standpoint of mechanics". In particular, in the second part of the course we will see the mathematics Einstein used in his paper from 1902.Besides, other concepts from Classical mechanics are explained, such as Liouville's theorem (this theorem is used by Einstein in his article), as well as Hamilton equations and more.For the second part, the student should already be familiar with phase space and other concepts from classical physics (such as Lagrange equations).Third part of the courseIn the third part of the course some of the articles of Einstein's Annus Mirabilis are explained. In particular, the article on the photoelectric effect and that on the Brownian motion.Fourth part of the courseIn the last section of this course we focus on the derivation of phase transitons from the Ising model. All the previous sections will be useful in contextualizing this last part of the course.
