Semiclassical Microlocal Analysis（2020 Fall）
中国科学技术大学数学科学学院
课程公告
(12/11) Lecture 21 uploaded.
(12/14) PSet 4 uploaded. Due: Dec. 28.
(12/18) Lecture 22-23 uploaded.
(12/23) Lecture 24-25 uploaded.
(12/23) Topics for course essay posted.Due: Jan. 22.
(12/30) Lecture 26, Lecture 27 uploaded.
(01/04) Lecture 28 uploaded.
(01/06) Lecture 29-30 uploaded.
课程信息
授课老师：
王作勤 (wangzuoq at ustc dot edu dot cn)
上课时间：
星期一下午 15:55 – 17:30; 星期三晚上 19:30 - 21:05
上课地点：
5304
办公室：
管研楼1601
参考教材
M. Zworkski，Semiclassical Analysis
参考教材
V. Guillemin and S. Sternberg, Semi-Classical Analysis
参考书籍
M. Dimassi and J. Sj\"ostrand, Spectral Asymptotics in the Semi-Classical Limit
参考书籍
A. Martinez, An Introduction to Semi-classical and Microlocal Analysis
参考书籍
G. Folland, Harmonic Analysis in Phase Space
参考书籍
B. Hall, Quantum Theory for Mathematicians
参考书籍
L. H\"ormander, The Analysis of Linear Partial Differential Operators III and IV
课程安排
课程安排可能会随着课程的进行而略有变动。
课程的讲义将在每堂课后上传。
作业将随课程进度不定时上传。
| 序号 | 日期 | 内容 | 讲义 | 习题 |
|---|---|---|---|---|
| Lecture 1 | 09/21 | Introduction; | Lect 1 | PSet 1: Due Oct. 19 |
| Lecture 2 | 09/23 | Classical v.s. quantum | Lect 2 | |
| Lecture 3 | 09/27 | Quantization and semiclassical limits | Lect 3 | |
| Lecture 4 | 09/28 | The Fourier transform | Lect 4 | |
| Lecture 5 | 09/30 | The method of stationary phase | Lect 5 | |
| Lecture 6 | 10/12 | PsDO I: Semiclassical quantization | Lect 6 | PSet 2: Due Nov. 16 |
| Lecture 7 | 10/14 | PsDO I: Weyl quantization | Lect 7 | |
| Lecture 8 | 10/19 | PsDO I: Weyl quantization via linear exponentials | Lect 8 | |
| Lecture 9 | 10/21 | PsDO I: The composition formula and quantization condition | Lect 9 | |
| Lecture 10 | 10/26 | PsDO I: Quantizating general symbols | Lect 10 | |
| 10/28 | Cancelled | |||
| Lecture 11 | 11/02 | PsDO II: L^2 boundedness | Lect 11 | PSet 3: Due Dec. 07 |
| Lecture 12 | 11/04 | PsDO II: compactness | Lect 12 | |
| Lecture 13 | 11/09 | PsDO II: Hilbert-Schmidt and Trace class | Lect 13 | |
| Lecture 14 | 11/11 | PsDO II: Invertibility | Lect 14 | |
| Lecture 15 | 11/16 | PsDO II: Positivity | Lect 15 | |
| Lecture 16 | 11/18 | PsDO III: generealized Sobolev Spaces | Lect 16 | PSet 4: Due Dec. 28 |
| Lecture 17 | 11/23 | PsDO III: Egorov theorem | Lect 17 | |
| Lecture 18 | 11/25 | PsDO III: h-PsDO with classical symbols | Lect 18 | |
| Lecture 19 | 11/30 | PsDO III: Differential operators on manifolds | Lect 19 | |
| Lecture 20 | 12/02 | PsDO III: h-Pseudodifferential operators on manifolds | Lect 20 | |
| Lecture 21 | 12/07 | Applications: The Eigenvalues/Eigenfunctions of h-Pseudodifferential operators | Lect 21 | Course Essay Topics: Due Jan. 22 |
| Lecture 22 | 12/09 | Applications: Weyl's Law | Lect 22-23 | |
| Lecture 23 | 12/14 | |||
| Lecture 24 | 12/16 | Applications: Quntum Ergodicity | Lect 24-25 | |
| Lecture 25 | 12/21 | |||
| Lecture 26 | 12/23 | FIO: Symplectic geometry backgrounds | Lect 26 | |
| Lecture 27 | 12/28 | FIO: Symplectic category | Lect 27 | |
| Lecture 28 | 12/30 | FIO: Enhanced symplectic category | Lect 28 | |
| Lecture 29 | 01/04 | FIO: Semiclassical Fourier integral operators | Lect 29-30 | |
| Lecture 30 | 01/06 | |||
| 01/09 | Online Minicourse: JIN Long （Tsinghua University） Quantum Chaos and Fractal Uncertanty Principle |
Abstract Slides | 14:00-16:00【202801247】【普朗克常数】 | |
| 01/11 | 16:00-18:00【930556440】【2\pi \hbar】 | |||
| 01/13 | 19:00-21:00【760787847】【662607】 |
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