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MATH-495: Mathematical quantum mechanics

Summary

Quantum mechanics is one of the most successful physical theories. This course presents the mathematical formalism (functional analysis and spectral theory) that underlies quantum mechanics. It is simultaneously an introduction to mathematical physics and an advanced course in operator theory

Lectures

Instructors

Official source

https://edu.epfl.ch/coursebook/en/mathematical-quantum-mechanics-MATH-495

Moodle Page

http://go.epfl.ch/MATH-495

About this result

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Summary

Lectures

Instructors

Official source

https://edu.epfl.ch/coursebook/en/mathematical-quantum-mechanics-MATH-495

Moodle Page

http://go.epfl.ch/MATH-495

About this result

Lectures in this course (30)

Function Spaces: Review and Compact Operators Log in to Mediaspace to watch this video

Covers the review of function spaces and explores the concept of compact operators.

Quantum Mechanics: Mathematical Framework Log in to Mediaspace to watch this video

Introduces the need for a mathematical framework to describe linear operators on infinite-dimensional Hilbert spaces in quantum mechanics.

Extension of Linear Transformations Log in to Mediaspace to watch this video

Covers the extension of bounded linear transformations and the free propagator in L^2 spaces.

Sobolev Spaces and Unitary Groups Log in to Mediaspace to watch this video

Explores Sobolev spaces, unitary groups, Laplacian properties, and translation groups in L^2.

Translation Groups on [0,1]Log in to Mediaspace to watch this video

Covers the study of translation groups on the interval [0,1] with different phases and the Riesz representation theorem on Hilbert space.

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