In this class, we discuss mostly the basic concepts in statistical mechanics, such as entropy, temperature, ensemble, ergodicity, phase transition. We also touch upon relevant frontier researches, for example, Bose-Einstein condensates and quantum H theorem. In addition, we discuss non-physics but related topics such income distribution in society and global warming.

Quantum mechanics was established in the early 20th century, and is one of the most profound revolutions in science history. It overthrows many basic concepts held sacred in classical mechanics, gives us an accurate description of behaviors of atoms, molecules, and other fundamental particles, and eventually bring us technological innovations that are deeply reshaping our human society. Despite its importance, quantum mechanics has remained a subject that is discussed only among physicists, some chemists, and a few philosophers. In recent days, quantum mechanics has become a subject frequenting social media as the result of the developments in quantum information.

This course is to introduce quantum mechanics both popularly and rigorously. By popular, it intends to be accessible to as many students as possible; by rigorous, it involves some advanced mathematics. It is impossible to accurately understand a scientific subject without mathematics. The course is designed for all students at Peking University, who should be skilled at high school mathematics. Any mathematics beyond high school level, such as matrix and linear algebra, will be covered in the course in a depth that is just enough to understand related quantum physics. To master and understand these advanced mathematical subjects, students are encouraged to do exercises left at the end of each class. No practice no understanding.

This course will tell a brief history of quantum mechanics, summarizing the breakthroughs made by the scientific heroes. After a short description of classical physics at the level of high school physics, the course begins to cover the following subjects: quantum states, quantum probability, superposition principle, quantum interference, quantum entanglement, Bell’s inequalities, quantum measurement and eventually quantum computing and quantum communications. I will also discuss how quantum and classical worlds are related and why we do not see quantum phenomena in our daily life and how quantum mechanics is covered in popular media.

Here are the lecture notes in Chinese.