Department of Physics

Summer Term 2022

14756.2024 | Advanced Quantum Mechanics

Hybrid Lectures
Lectures will be in presence, pandemic situation permitting (Monday 10.00-11.30 and Thursday 08.00-09.30, HS III). Live participants need to obey the rules imposed by the University of Cologne. There will also be a zoom live stream/recording of the lectures, which can be accessed via ILIAS.

There is a Slack workspace to discuss among students and with the lecturer/tutors and to publish the weekly exercise sheets. Please write an email to Thomas Müller to register.

Tutorials
Tutorials will be held on Wednesdays, three in hybrid mode, and one fully online. Please check the information sheet for further details.

Contact:
Dr. Johan Aberg (johan.aberg [at] uni-koeln [dot] de)
Dr. Romain Daviet (daviet [at] thp.uni-koeln [dot] de)
Thomas Müller (tmueller [at] thp.uni-koeln [dot] de)
Mark Goh (xgoh [at] smail.uni-koeln [dot] de)
Saurabh Kumar (skumar [at] thp.uni-koeln [dot] de)
Rohan Mittal (rmittal1 [at] smail.uni-koeln [dot] de)

Lecture Materials
Script
Further informations

In order to access the materials you need to be connected to the university network via VPN: see details on the RRZK website .

Contents
Scattering theory: Scattering cross section; Lippmann-Schwinger equation, Green’s function, T- and S-matrix; optical theorem; Born approximation; centrosymmetric potential scattering, low energy scattering and scattering length, ultracold atom scattering and Feshbach resonances; time reversal in quantum mechanics (scattering theory is more fun than you might guess!).
Canonical Quantization: Qubits and electromagnetic fields: Physics and quantization of superconducting circuits, driven systems, rotating frame transformation, reduction to qubit Hamiltonian; quantization of classical electrodynamics coupled to non-relativistic matter, reduction to Jaynes-Cummings model, semiclassical limit, Rabi oscillation revivals, spontaneous emission and irreversible decay, inelastic light scattering.
Second Quantization: Bosons and fermions: Indistinguishable particle postulate, bosons and fermions, many-particle Hilbert space and Fock space; Representation of single- and two-particle operators in Fock space; quantum dynamics of field operators; applications: Bose-Einstein condensation of weakly interacting ultracold bosonic atoms, Gross-Pitaevskii equation and Bogoliubov theory; quantum phase transition of fermions and spins in one dimension.
Relativistic quantum mechanics and Dirac equation: Recap on special relativity and Lorentz group; Klein-Gordon equation; gauge invariance; Dirac equation: solutions and interpretation; non-relativistic limit; quantization of the Dirac field.

Literature
Is specified in the script.