Module

Voraussetzungen

Inhalte

• Theory of unbounded linear operators • Hermitian and self-adjoint operators • Resolvents and the spectral set of unconstrained operators • Spectral theorem of self-adjoint operators • Theorems of E. Helly • Spectral theorem for unitary operators • Time-dependent Schrödinger equation • The Friedrichs continuation for semi-constrained Hermitian operators • Elliptic differential operators and Schrödinger operators with their spectra

Lernziele

After successfully completing the module, students have mastered the mathematical fundamentals of linear spectral theory. They are able to determine independently when linear operators have a discrete or continuous spectrum. The students know in detail special classes (e.g. the class of Schrödinger operators) of linear operators, which play an important role in other areas of mathematics and physics. In addition, they have expanded their knowledge of analysis.

Prüfungsleistung

• oral examination, 30 minutes

Bemerkungen

• Study programme Angewandte Mathematik M.Sc.: Compulsory elective module in the complex „Analysis/Algebra/Kombinatorik“ • Study programme Mathematics M.Sc.: Compulsory elective module in the complex „Analysis/Algebra/Combinatorics“