Perturbation Theory for Operators

Garant předmětu:

Lecturer:

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Department of Mathematics

Synopsis:

The focus is put on the regular and asymptotic perturbation theory for linear operators.

Requirements:

Syllabus of lectures:

1. Perturbationtheory in afinite-dimensionalspace, roots ofpolynomialsanalytically dependingon aparameter, a Puiseuxseries, Rellich’s theorem, Rayleigh-Schrödingerseries.2. Regularperturbationtheory, analyticfamily ofoperatorsin the sense ofKato, the Kato-Rellichtheorem, analyticfamily ofoperatorsof type(A) and(B).3. Asymptotic perturbationtheory, asymptotic series, theanharmonic oscillatoras an example.4. Resonancesand the Fermi golden rule.

Syllabus of tutorials:

Study Objective:

Study materials:

Key references: [1] M. Reed, B. Simon: Modern Mathematical Physics IV: Aanalysiz of Operators, Academic Press, New York, 1978(kapitola XII).[2] T. Kato: Perturbation Theory for Linear Operators, Springer-Verlag, New York, 2013 (kapitola II).[3] G. Teschl, Mathematical Methods in Quantum Mechanics: With Applications to Schrodinger Operators, 2nd edition, American Mathematical Society, 2014.Recommended references:[4] E. Brian Davies: Linear Operators and their Spectra, Cambridge University Press, Cambridge, 2007.[5] J. Weidmann: Linear Operators in Hilbert Spaces, Springer-Verlag, New York, 2013.

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Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: