# Fortgeschrittene Quantentheorie

MSc Physik

Wintersemester 2024/25

### Lecturer

### Begin of course

The lecture will start already in the first week of the semester, i.e., the first class will take place on **Thursday, 17. October 2024**. The exercise classes will start in the second week (week of October 21).

### Spacetime

- Thursday, 11:30 - 13:00, Hörsaal V57.02, Pfaffenwaldring 57
- Friday, 11:30 - 13:00, Hörsaal V57.
**05**, Pfaffenwaldring 57

### General Information

- The lecture will be given in
**German**. - Importantly, if you are a student in the international masters program, you have to attend the international master's version of this course, see here for further information.
- The registration for the exercise groups will be open from
**Friday, 18. October 2024, 13:30**. To do so, you need the**Lecture Key**given in the second lecture. Note that the registration is only possible from within the university network. - If you assign a password at the registration, you can request your current scores here.

**Recordings **of the lectures can be accessed via ILIAS. The recordings should be seen as a service to those of you who cannot come on a specific date (e.g., due sickness etc.) or want to recap later. However, I highly recommend attending as many lectures as possible, to take advantage of the interactive nature of the classroom and learn with/from your peers.

### Examination

There will be a **written exam** at the end of the course (12.03.25, time will be announced) on the content covered by the lecture. The exam will be 2h and you will be allowed to bring one A4 page (only one side) with handwritten notes.

To **qualify** for the written exam, you have to pass the exercise class (see below). Students who have already obtained a suitable certificate from another lecturer must have it recognized by 31.01.2025 by sending it via E-Mail to Prof. Scheurer.

### Literature

- Messiah,
*Quantenmechanik Band**1*&*2*. - Nolting,
*Grundkurs Theoretische Physik 5/1 & 5/2.* - Sakurai,
*Modern Quantum Mechanics*and*Advanced Quantum Mechanics*. - Cohen-Tannoudji,
*Quantenmechanik**Band 1-3*. - Schwabl,
*Quantenmechanik*&*Quantenmechanik für Fortgeschrittene*. - Le Bellac,
*Quantum Physics*.

Compact review of many topics of basic and advanced quantum mechanics: Münster*, Quantentheorie*.

### Topics

**Chapter 1 – Review of Basics of Quantum Theory.** Mathematical foundation. Time-dependent and -independent Schrödinger equation. Heisenberg picture. Basis transformations. Observables. Heisenberg uncertainty relation. Particle in a box and harmonic oscillator.

**Chapter 2 – Symmetries.** Definition and consequences. Parity. Translational symmetry and Bloch theorem. Rotations and angular momentum operator. Additional of angular momenta. Time-reversal symmetry.

**Chapter 3 – Approximate Methods.** Non-degenerate and degenerate stationary perturbation theory. Variational principle and methods. Semi-classical approximation and WKB. Time-dependent perturbation theory. Fermi's Golden rule. Diabatic and adiabatic evolution.

**Chapter 4 – Quantum Many-Body Physics.** The many-body Hilbert space. Harmonic chain. Quantizing the electromagnetic field. Light-matter interaction. Identical particles. Second quantization. Hartree-Fock.

**Chapter 5 – Relativistic Quantum Mechanics.** Review of classical relativistic mechanics. Klein-Gordon equation. Dirac equation. Non-relativistic limit.

### Requirements to pass exercise class

The weekly exercises class will involve:

(1) **Handing in solutions** for those exercises labeled as "written"; these will be marked and discussed in the next tutorial. The **deadline** is **Tuesday at 6:00 PM** of the week where the problem set will be discussed. Please upload your solutions on ILIAS before the deadline.

(2) **Virtual presentations**: at the beginning of every tutorial, you can indicate on a list which parts of the exercises labeled as "oral" you have prepared and are willing to present. While everyone will get points for the parts signed up for, only one person will have to present it.

If any question on the exercise lists is not clear enough, please feel free to contact Subrata Mandal for clarifications.

In order to **pass the exercises**, you need at least 50% of the points in (1) and 66% of the points in (2); furthermore, every student is required to present at least three times on the blackboard.

### Numerical illustrations

To visualize content of the lecture I will sometimes use Wolfram Mathematica. The files shown in the lecture will also be made available to you via ILIAS. While you are encouraged to play with them on your own computer, the ability to write code is not required for the assessment of the lecture. You can display the Mathematica files on your computer using the Wolfram Player for Notebooks.

### Problem Sets

No. | Published | Due | Download | Comments |
---|---|---|---|---|

1 | 15.10.24 | 22.10.24 | Problem Set 1 | |

2 | 22.10.24 | 29.10.24 | Problem Set 2 | |

3 | 29.10.24 | 05.11.24 | Problem Set 3 | |

4 | 05.11.24 | 12.11.24 | Problem Set 4 | |

5 | ||||

6 | ||||

7 | ||||

8 | ||||

9 | ||||

10 | ||||

11 | ||||

12 | ||||

13 | ||||

14 |

### Tutorials

Tutor | Room | Day | Time |
---|---|---|---|

Sayan Banerjee | 4.331 | Thursday | 14:00 |

Subrata Mandal | 5.331 | Thursday | 15:45 |

João Sobral | 5.331 | Friday | 08:00 |

Bernhard Putzer | 5.331 | Friday | 09:45 |

Lucas Pupim | 2.150 | Friday | 09:45 |

Denis Sedov | 2.552 | Friday | 09:45 |