Goals of the Course(JPN)
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.
Objectives of the Course(JPN))
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).
Course Content / Plan
1) Hilbert space and linear operators
2) Scattering theory: time dependent approach
3) Scattering theory: time independent approach
4) Scattering theory: stationary expressions
|Knowledge on standard undergraduate linear algebra, calculus and advanced calculus.
|Any courses on functional analysis.
Course Evaluation Method and Criteria
|Grades based on attendance and on written reports. An active participation of the students is expected.
|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.
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
Notice for Students
|Additional information and material will be added regularly on
Propriety of Other department student's attendance
Conditions of Other department student's attendance
|This course is open for any students at Nagoya University. Motivated undergraduate students are also welcome.
|Spectral and scattering theory, unitary operators
|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.
Lecture format, etc.
|Face-to-face in room 309 of the math building
Additional measures for remote class (on-demand class)