Spectral Theory - An introduction to Mathematical Methods of Quantum Mechanics, 7.5 ECTS

Second level

Description

The course covers linear operators in Hilbert space in relation to quantum mechanics: Hilbert space geometry, compact operators, integral operators and the Fredholm Alternative, unbounded operators, adjoint operators, extension theory for symmetri…

The course covers linear operators in Hilbert space in relation to quantum mechanics: Hilbert space geometry, compact operators, integral operators and the Fredholm Alternative, unbounded operators, adjoint operators, extension theory for symmetric operators, spectral theory for Schrödinger operators, elementary perturbation theory.

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Area of interests: Information only in Swedish

Information only in Swedish

Subject

Mathematics

As a mathematical theory always implies that certain conclusions hold under certain given conditions, it can in principle say nothing about the physical reality. None the less mathematics has become an indispensable tool for a large number of subjects like astronomy, physics, chemistry, statistics and the technical sciences and in later times also for economy, biology, various social sciences and computor science. The role of mathematics in the applied sciences is both to supply notions for exact and adequate formulations of empirical laws but also from these laws to derive consequences, which can be used to find better models of the reality one has to describe. These tasks have lately become more important. Mathematics is in continual progress by intensive international research, new theories are created and already existing theories are simplified and augmented.

Mathematics

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