Mathematical Methods for Quantum Mechanics and Quantum Control

Summer 2024

Abstract: The subject of this seminar is an overview on methods of linear algebra and functional analysis required for the description of the free and controlled dynamics of quantum systems. These will include limit theorems for finite and infinite-dimensional quantum systems (Zeno limit, Trotter product formulas, adiabatic theorems, rotating-wave approximations), theory of self-adjoint extensions of unbounded symmetric operators, and relation between the spectrum of self-adjoint operators and the induced dynamics.

People: Daniel Burgarth, Davide Lonigro.

Time and place: The seminar runs weekly every Friday at 14:15–16:00 in the Seminarraum Theoretische Physik II (Department of Physics, Floor 2). The course is in English.

Seminar Schedule: The schedule of the seminar can be found here; you will also find here an overview of the topics. Each student should arrange an individual meeting with us to discuss the scope of the talk and to obtain some references by sending an e-mail to daniel.burgarth@fau.de and davide.lonigro@fau.de no later than three weeks before their seminar.

References for the introductory lecture:

G. Teschl, Mathematical Methods in Quantum Mechanics. With Applications to Schrödinger Operators. Graduate Studies in Mathematics, Volume 157, Amer. Math. Soc., Providence, 2014.

The book can be freely downloaded here. More detailed references are given in its introduction, page xii.B. Hall, Quantum Theory for Mathematicians. Springer, 2013.