授業の目的 【日本語】
Goals of the Course(JPN) | | |
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授業の目的 【英語】
Goals of the Course | | Title : Scattering theory for unitary operators
In this course, we shall develop the scattering theory for unitary operators, mimicking the better developed theory for self-adjoint operators. The time dependent and time independent approach will be studied, and stationary expressions for the main objects of scattering theory will be constructed. With this subject, we shall also pay tribute to the seminal work of Kato and Kuroda on scattering theory. |
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到達目標 【日本語】
Objectives of the Course(JPN)) | | |
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到達目標 【英語】
Objectives of the Course | | | Understand the role of scattering theory as a comparison theory and develop the necessary tools for applying this theory in various contexts (from dynamical systems to group representations). |
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授業の内容や構成
Course Content / Plan | | Content (preliminary)
1) Hilbert space and linear operators
2) Scattering theory: time dependent approach
3) Scattering theory: time independent approach
4) Scattering theory: stationary expressions |
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履修条件
Course Prerequisites | | | Knowledge on standard undergraduate linear algebra, calculus and advanced calculus. |
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関連する科目
Related Courses | | | Any courses on functional analysis. |
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成績評価の方法と基準
Course Evaluation Method and Criteria | | | Grades based on attendance and on written reports. An active participation of the students is expected. |
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教科書・テキスト
Textbook | | |
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参考書
Reference Book | | W. Amrein, Hilbert space methods in quantum mechanics, EPFL press, 2009.
W. Amrein, Non-relativistic Quantum dynamics, Reidel Publishing Company, 1981.
H. Baumgartel, M. Wollenberg, Mathematical scattering theory, Birkhauser, 1983.
T. Kato, Perturbation theory for linear operators, Springer, 1995.
D. Yafaev, Mathematical scattering theory: general theory, AMS, 1992.
D. Yafaev, Mathematical scattering theory: analytic theory, AMS, 2010. |
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課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours) | | | Students are supposed to read their notes between two lectures. The subjects of the reports can be chosen according to the interest of the students |
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注意事項
Notice for Students | | Additional information and material will be added regularly on
http://www.math.nagoya-u.ac.jp/~richard/Unitary.html |
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他学科聴講の可否
Propriety of Other department student's attendance | | |
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他学科聴講の条件
Conditions of Other department student's attendance | | | This course is open for any students at Nagoya University. Motivated undergraduate students are also welcome. |
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レベル
Level | | |
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キーワード
Keyword | | | Spectral and scattering theory, unitary operators |
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履修の際のアドバイス
Advice | | | It is certainly easier to attend a course in English and to discuss in this language in a quiet university environment rather than later in a busy life. |
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授業開講形態等
Lecture format, etc. | | | Face-to-face in room 309 of the math building |
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遠隔授業（オンデマンド型）で行う場合の追加措置
Additional measures for remote class (on-demand class) | | |
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