Advanced Quantum Theory

Lecture (MVAMO2)

Thomas Gasenzer

Thursday, 11:15-13:00 (starting on 21/04); INF 227 (KIP), SR 3.403+4. [LSF]

Additional lectures: Tuesday, 10/05 and 24/05; 14:15-16:00; INF 227 (KIP), SR 1.403+4.

Head tutor: Asier Pineiro Orioli

Register and view group list here.
Classes take place in general during even weeks on Tue, 14:15 - 16:00: INF 227 (KIP), SR 1.404; Tue, 16:15 - 18:00: INF 227 (KIP), SR 2.402; starting on 03/05/16.

Written exam on Wed, 27/07/15, 11:00-13:00 hrs, INF 227 (KIP), SR 3.403+4.

Content - Prerequisites - Script - Literature - Supplementary materials - Exercises - Exam

The lecture course provides an introduction to advanced quantum theory within the specialisation module Atomic, Molecular, and Optical Physics. From the MSc-Module handbook: After completing this course the students will be able to - describe the fundamental concepts of quantum physics and the relevant theoretical methods, - analyse standard experimental approaches using the relevant theoretical methods, - solve problems in quantum physics and quantum optics, - apply the relevant theoretical methods to model concrete physical situations.

Content (prelim.):
  1. Introduction
    - A brief reminder of some basics of quantum mechanics
  2. Quantum theory of matter
    - From classical to quantum fields - Lagrangian and Hamiltonian field theory - *Constrained quantisation - Quantisation of the Bose field - Mode expansion - Harmonic oscillator - One- and multiparticle operators - Fock space - Identical particles - Bosons and fermions - Coherent states - Wigner function and phase space
  3. Interactions
    - Born-Oppenheimer Approximation - H+
    and H2 molecules - Potential scattering - Scattering of a wave packet - Green's function and Lippmann-Schwinger equation - Scattering cross section - Partial-wave analysis - S-matrix and scattering phase - *Long-range potentials - Low-energy scattering and s-wave approximation - Optical theorem - Square-well potential: s-wave scattering length, effective range - *Resonance scattering
  4. Theory of quantum states
    - Density operator - Pure states and mixed ensembles - Environment and partial trace - The measurement process - Alternative approaches - Entanglement - Einstein-Podolsky-Rosen Paradoxon - Bell’s inequalities
  5. Open quantum systems
    - Quantization of the electromagnetic field - Interaction of atoms with electromagnetic vacuum - The Jaynes-Cummings model - Collapse and revival - Open quantum systems - Dissipation in classical systems - Master equation - Spontaneous Emission - Decoherence

Skriptum :

Textbooks on Quantum Mechanics (in alphabet. Order): Classics: Publicly accessible scripts: Classical Mechanics Quantization subject to (gauge) constraints Scattering theory General texts on quantum optics For further reference: A few general texts on quantum field theory Additional material

Exercises will be during even weeks on Tue, 14:15 - 16:00: INF 227 (KIP), SR 1.404; Tue, 16:15 - 18:00: INF 227 (KIP), SR 2.402; starting on 03/05/16. Tutors: Raphael Beinke and Salvatore Castrignano (Please register here.)

Problem Sheets will be available for download here.


Passing the written exam, which will prospectively take place on Wed, 27/07/15, 11:00-13:00 hrs, INF 227 (KIP), SR 3.403+4, will be the condition to obtain 4 CPs for the lecture.
Rules for the exam: You are allowed to use one A4 two-sided and handwritten sheet. No electronic devices of any kind are permitted. The exam lasts 120 mins. Please bring enough paper to be able to start every problem on a new sheet of paper.