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開講年度・開講期 前期
授業形態 講義
配当学年 全回生
対象学生 Undergraduate
曜時限 月3
教員
  • 青谷 正妥(アオタニ マサヤス)(国際交流推進機構)
授業の概要・目的 (授業のテーマと目的)
[An Important Note]
In the following, descriptions and explanations in Japanese apply only to Japanese students and other regular Kyoto University students. Exchange students should ignore the Japanese text. A few words about the instructor’s background in physics are due as his BS was in Chemistry, Ph.D. was in Mathematics, and Ed.D. was in English Education. Despite the names of the degrees he has, he learned quantum mechanics rather extensively from Professors Alexander and Park at the University of Maryland, Witten and Rabitz at Princeton University, and Onishi at the City College of the City University of New York. His thesis advisor at UC Berkeley, the late William Arveson, was known for his major contributions related to von Neumann algebras, which are very important in quantum mechanics. In fact, the instructor has taken many more courses in Physics than in Mathematics. He also served as a graduate student instructor in Physics and Astronomy at UC Berkeley. He is fully qualified to teach this course.

[Another Important Note]
My lecture notes, available at http://aoitani.net/Modern_Physics_2014.pdf, contain far more materials than what we actually cover in the class. Many topics are too advanced for the typical audience. However, my notes are supposed to be a complete, self-contained reference. Questions on the final examination will be much simpler as you can see at http://aoitani.net/ Final_Examination_2013.pdf.

[重要]
日本人及び正規生の方は、日本語の説明を読んで下さい。英語は交換留学生用の説明です。 尚、講師の学士は化学、博士は数学ですが、量子力学ではMaryland大学のAlexanderとPark、Princeton大学のWittenとRabitz、NY市立大学のOnishiに師事し、博士論文指導教官の故William Arvesonは数学者ですが、von Neumannの流れで量子論関連の貢献も種々 有ります。実は、人生を通して取った単位は物理の方が数学より5割がた多いうえ、UC Berkeleyでは院生時代に物理学や天文学を教えていたので信用して頂いて大丈夫です。

[続重要]
講義ノートは http://aoitani.net/Modern_Physics_2014.pdf にあるのですが、これだけで独立した完全な教科書兼参考書ですので、授業で扱わないような高度な内容も入っています。実際の試験はこれよりずっと簡単です。ここを見て下さい。http://aoitani.net/ Final_Examination_2013.pdf

Course Objective
The purpose of this course is to introduce engineering and science students to the foundations, principles, and applications of quantum mechanics. This course is based on the two classes I took from Edward Witten at Princeton University in the early eighties and the approach advocated by Ramamurti Shanker of Yale University. Together, the exposition will enable a smooth transition to quantum field theory.

In order to get an idea as to what it looks like, please check the thorough book-length lecture notes available at http://aoitani.net/Modern_Physics_2014.pdf. I am in the process of making this into a book, but this working version is free! 

理系の学生の為の、現代物理学の根幹を成す量子力学の基礎理論と応用の講義です。 講師が80年代初頭にプリンストン大学でかのEdward Wittenから取った二つの講義と、エール大学のRamamurti Shankerのアプローチに基づいた解
説で、量子場の理論へのつながりを視野に入れた講義をします。

興味のある人は、授業で配布される講義ノートを見てみてください。出版準備中ですが、これはただです。
http://aoitani.net/Modern_Physics_2014.pdf
授業計画と内容 Overview
We will study the main concepts of quantum mechanics developed since around the turn of the 20th century. The overall learning objective is to acquire the contextualized knowledge and analytic skills necessary to construct an understanding of phenomena in the domain of quantum mechanics. To this end, we will cover the following topics.

概要
量子力学の主要概念を学び、量子力学的現象を正しく理解する為の、知識のフレームワークと解析的能力を身に付けます。

Topics Covered
0. Mathematical Preliminaries
Inner Product Space, Dirac’s Bra-and-Ket Notation, Linear Operators, Commutator, Hermitian, Anti-Hermitian, and Unitary Operators, Eigen Value Problems, Propagator, Functions and Derivatives of Operators, Infinite Dimensions
1. Crises in Classical Physics: High Speed; Microscopic Phenomena
2. Planck and Blackbody Radiation
3. Einstein and Photoelectric Effect
4. Compton and Rutherford Scattering
5. Bohr Model
6. De Broglie’s Matter Waves
7. Birth of Quantum Mechanics
8. Schroedinger Equation
9. Square Well Potential
10. Scattering in One dimension
11. Simple Harmonic Oscillator
12. Electron Spin
13. Spectroscopy
14. Other Applications

主な内容
0. 数学的基礎
ヒルベルト空間、ディラックのブラとケット、線形オペレーター、交換関係、エルミート・反エルミート・ユニタリー演算子、固有値、Propagator、演算子の関数・微分、無限次元
1. 古典物理学の破綻:高速現象、微視的現象
2. マックス・プランクと黒体輻射
3. アインシュタインの光電効果
4. コンプトン、ラザフォード散乱
5. ボーアモデル
6. ド・ブロイの物質波
7. 量子力学の誕生
8. シュレーディンガー方程式
9. 井戸型ポテンシャル
10. 一次元の散乱
11. 調和振動子
12. 電子スピン
13. 分光法
14. その他の応用
成績評価の方法・観点 There will be a final examination.

期末テストが有ります。
履修要件 Prerequisite
Mastery of high school physics and mathematics at the level necessary to pass Kyoto University's entrance examination is required. This means mathematics through calculus and non-calculus-based high school physics.

高校の理系の数学、及び、理系の物理学。
教科書
  • No required text. Thorough book-length lecture notes will be provided. http://aoitani.net/Modern_Physics_2014.pdf. 指定教科書無し。微に入り細を穿った講義ノート(上記URL)が配布されます。
参考書等
  • Quantum Physics: Of Atoms, Molecules, Solids, Nuclei, and Particles 2nd edition (January 1985), Robert Martin Eisberg and Robert Resnick, (John Wiley & Sons), ISBN: ISBN:047187373X
関連URL
  • http://aoitani.net/aotani-KKyoto.html