Advanced Quantum Theory

summer term 2023
Lecturer: Haverkort
Link to LSF
53 participants
In this lecture we will discuss the quantum theory of matter and light. We will start by introducing the Dirac equation. After we discuss the basic ideas how Dirac came to introduce this equation and show that the equation makes sence, we will look at the soltion of the hydrogen atom. If we include the electro magnetic field into the Dirac equation we find that the eigen-states are mixed states with different photon number. This leads to the Lamb shift.
We will investigate the interaction between light and matter in more detail by looking at the example of an hydrogen atom in an oscillating external electromagnetic field. If the atom starts in the ground-state then the light field can excite the atom. If the energy of the photons is equal to the energy of an excited state in the atom the transition rate is given by Fermi's golden rule, which we will derive. Experimentally atoms also absorb and scatter photons whose energy does not correspond exactly to the energy differences between eigenstates. This effect can be understood with response theory. We will compare the classical response functions to the onces obtained in quantum mechanics. The later are known as Kubo's formula. Kubo's results will be generalised and we will introduce the concept of Feynman diagrams and self energy.
The theoretical tools introduced in this lecture will be applied to one electron atoms (hydrogen) in the relativistic (Dirac equation) and non-relativistic limit (Schrödinger equation) as well as to multi-electron systems. For many electron systems we will discuss concepts like entanglement and correlations as well as quantum fluctuations. The later will be compared to temperature fluctuations.
The module consists of one lecture per week and a biweekly tutorial session. At the end of the semester there will be a written examination. 


Practice groups

  • Group 1 (Natalia Oreshkina)
    13 participants
    INF 227 / SR 3.403, Tue 14:15 - 16:00
  • Group 2 (Chen Xin)
    10 participants
    Philos.-weg 12 / kHS, Wed 14:15 - 16:00
  • Group 3 (Félix Rose)
    20 participants
    INF 227 / SR 2.402, Wed 16:15 - 18:00
  • Group 4 (Mrinal Sarkar)
    10 participants
    Philoso.-weg 12 / kHS, Tue 14:15 - 16:00

Material discussed


17.04.2023 Chapter 11 of the script. Introduction to the Dirac equation.
24.04.2023 Chapter 11 of the script. Non-relativistic limit of the Dirac equation.
1.05.2023 No Lecture
8.05.2023 Chapter 11 of the script. Relativistic solutions to the Dirac equation and introduction to the Lamb shift.
29.05.2023 No Lecture
26.06.2023  Response theory, relation between frequency and time domain. Kramers Kronig relation
3.07.2023  Response theory, relation between frequency and time domain. Kramers Kronig relation
10.07.2023 Decoherence and quasi-particle lifetime 
17.07.2023 Free time to study
24.07.2023 Exam
31.07.2023 Discussion of exam results
Advanced Quantum Theory
summer term 2023
Link zum LSF
53 participants
  • The lectures will be on Monday from 14:15 to 16:00 in INF 227 HS2. The first lecture is on Monday the 17th of April.
  • The tutorials will be biweekly, starting in the week of the 24th of April. 
  • I higly recommend you to be present in the lecture hall. For those who can not come we will stream the lectures via Zoom.
  • After some time the lectures will apear on Youtube.  (We will filter out all voices of students present in the room)
  • The exam will be on Monday the 24th of July from 14:15 to 17:00 in INF227 HS2.