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課程名稱 |
微分幾何及其在物理的應用
Introduction to differential geometry for physicists |
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開課學期 |
100-2 |
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授課對象 |
理學院 物理學研究所 |
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授課教師 |
胡崇德 |
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課號 |
Phys5045 |
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課程識別碼 |
222 U2180 |
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班次 |
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學分 |
2 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期五6,7(13:20~15:10) |
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上課地點 |
新物833 |
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備註 |
「開放式課程」。
總人數上限：20人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1002diffgeo |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
Introduction to tensor analysis in curvilinear coordinate systems, differential forms, differential geometry, Berry's phase and other applications of geometrical ideas in physics |
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課程目標 |
To prepare the students for modern differential and integral calculus and their applications in modern physics. |
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課程要求 |
修過應用數學一、應用數學二、應用數學三或高等微積分
elementary quantum mechanics |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
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參考書目 |
"Mathematical Methods for Physicists", by Arfken and Weber, 6th Edition, Sections 2.10, 2.11, 4.8
“Differential Forms with Applications to the Physical Sciences”, by Harley Flanders,
“Mathematical Methods of Physics”, by Mathews and Walker, 2nd Edition, Chapter 15
“Modern Quantum Mechanics”, by J. J. Sakurai, Revised Edition, Supplement I: Adiabatic Change and Geometric Phase
"Solid State Physics", by Grosso and Parracivini, Chapter VIII
“A Mathematical Gift, I”, by K. Ueno, K. Shiga and S. Morita, Chapter 1: Invitation to Topology
“Studies in Global Geometry and Analysis”, by S. S. Chern
"Geometry, Topology and Physics", by M Nakahara
“Topology and Geometry for Physicists”, C. Nash and S. Sen
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Homework |
50% |
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2. |
Presentation |
20% |
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3. |
Exam |
30% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/24 |
Organizational meeting, course overview |
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第2週 |
3/02 |
Euler characteristic, curvature of surface |
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第3週 |
3/09 |
Intuitive discussion of Gauss-Bonnet , Poincare-Hop theorems |
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第4週 |
3/16 |
Adiabatic principle and Berry phase |
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第5週 |
3/23 |
Berry’s curvature-analysis and topology |
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第6週 |
3/30 |
Classical tensor analysis, connection and curvature
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第7週 |
4/06 |
Model of gauge interaction in electronic-nuclear systems |
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第8週 |
4/13 |
Differential forms |
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第9週 |
4/20 |
Homology and cohomology groups
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第10週 |
4/27 |
Spin Hamiltonians and fiber bundles
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第11週 |
5/04 |
Differential geometry of surface |
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第12週 |
5/11 |
Global geometry of surface |
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第13週 |
5/18 |
Geometry of fiber bundles
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第14週 |
5/25 |
Characteristic classes |
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第15週 |
6/01 |
Harmonic forms |
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第16週 |
6/08 |
Index theorem-application to polyacetylene and graphene |
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第17週 |
6/15 |
Review |
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