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- Academic unit or major
- Mathematics
- Instructor(s)
- Mizutani Haruya Kagei Yoshiyuki
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Intensive (本館2階数学系201セミナー室)
- Group
- -
- Course number
- ZUA.E336
- Credits
- 2
- Academic year
- 2022
- Offered quarter
- 4Q
- Syllabus updated
- 2022/4/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
This is an introductory course of mathematical study of the quantum scattering theory, which studies the asymptotic behaviors of solutions to some PDEs describing the motion of microscopic particles such as Schroedinger or Dirac equations. The first half of the course will be devoted to explaining the spectral theory for Self-adjoint operators and the existence and asymptotic completeness of wave operators for short-range Schrodinger equations, while the latter half part will be concerned with the boundedness of wave operators on Lebesgue spaces as an application of scattering theory to PDEs.
The goal of the lecture is to learn basic knowledge and techniques of analysis in the mathematical study of quantum scattering theory.
Student learning outcomes
To learn some basic techniques of Functional analysis in the spectral theory.
To understand the basic framework of mathematical quantum scattering theory.
Keywords
Quantum scattering theory; Spectral theory; Self-adjoint operator; Schroedinger equation; Wave operator; Asymptotic completeness
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This is a standard lecture course. There will be some assignments.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | The following topics will be discussed (as long as time allows): ・Basic framework of Quantum scattering theory ・Spectrum of self-adjoint operators and RAGE theorem ・Limiting absorption principle for the resolvent and Mourre theory ・Smooth perturbation theory ・Existence and asymptotic completeness of wave operators for short-range Schroedinger equations ・Boundedness of wave operators on Lebesgue spaces | Details will be provided during each class session. |
Textbook(s)
None required
Reference books, course materials, etc.
黒田成俊「スペクトル理論II」岩波書店
中村周「量子力学のスペクトル理論」共立出版
谷島賢二「シュレーディンガー方程式 I, II」朝倉書店
磯崎洋「多体シュレーディンガー方程式」丸善出版
Other references will be announced in the lecture.
Assessment criteria and methods
Assignments (100%).
Related courses
- MTH.C351 ： Functional Analysis
- MTH.C305 ： Real Analysis I
- MTH.C306 ： Real Analysis II
- MTH.C341 ： Differential Equations I
- MTH.C342 ： Differential Equations II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None
