Introduction to mathematical physics, fall 2010

Spectral theory

Lecturer

Jani Lukkarinen

Scope

10 cu.

Type

Advanced studies. Very suitable as a continuation of Introduction to functional analysis (Funktionaalianalyysin peruskurssi)

Description

The course focuses on derivation and applications of spectral theory of operators on a Hilbert space. The mathematical topics will include Banach algebras and spectral measures of unbounded operators, and applications will be mainly chosen from physics, in particular, from quantum mechanics

Prerequisites

Basic measure theory and functional analysis

Lectures

Tue 14-16 and Thu 14-16, Exactum room C123. On weeks 36-41, 44, and 46-50

Bibliography

• Course lecture notes
• W. Rudin, Functional Analysis, McGraw-Hill, 2nd edition, 1991
• M. Reed, B. Simon, Methods of Modern Mathematical Physics I: Functional Analysis & II: Fourier Analysis, Self-Adjointness, Academic Press, 1980 & 1975
• G. Teschl, Mathematical Methods in Quantum Mechanics; With Applications to Schrödinger Operators, Graduate Studies in Mathematics 99, Amer. Math. Soc., 2009
• T. Kato, Perturbation Theory for Linear Operators (Classics in Mathematics), Springer, 2008
• O. Bratteli, D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics 1 & 2, Springer, 2002 & 2002

Registration

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Exercise groups

Problem sheets

Lecture notes