# Advanced Quantum Theory

MSc Physics

Winter Semester 2023/24

### 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, 19. October 2023**. The exercise classes will start in the second week (week of October 23).

### Spacetime

- Thursday, 11:30 - 13:00, Seminar Room 5.331, Pfaffenwaldring 57
- Friday, 11:30 - 13:00, Seminar Room 5.331, Pfaffenwaldring 57

### General Information

- The lecture and the tutorials will be given in
**English**. - The registration for the exercise groups will be open from
**Friday, 20. October 2023, 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 an individual **30 mins oral exam** at the end of the course. You can choose which topic (i.e., one of the five chapters in the list of topics below) the first few questions will be about, but should expect that any topic covered in the lecture can be part of the exam. The available dates will be discussed towards the end of the semester. I plan to offer exams in the first two weeks of the semester break and close to the end of it before the summer term begins.

To be able to take the oral 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 01.02.2024 by sending it via E-Mail to Prof. Scheurer.

### Literature

- Messiah,
*Quantum Mechanics**Vol. 1*and*2*. - J. Sakurai,
*Modern Quantum Mechanics*and*Advanced Quantum Mechanics*. - Cohen-Tannoudji,
*Quantum Mechanics**Volume 1-3*. - Schwabl,
*Quantum Mechanics*and*Advanced Quantum Mechanics*. - Le Bellac,
*Quantum Physics*.

### Topics

**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.**Symmetries.**Definition and consequences. Parity. Translational symmetry and Bloch theorem. Rotations and angular momentum operator. Additional of angular momenta. Time-reversal symmetry.**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.**Quantum Many-Body Physics.**The many-body Hilbert space. Harmonic chain. Quantizing the electromagnetic field. Identical particles. Second quantization. Hartree-Fock.**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 **Wednesday at 17:00** of the week where the problem set will be discussed. The preferred way of handing in the solutions is via upload on ILIAS. Alternatively, you can hand them in in person in room 5.350 on Tuesdays between 9:00 AM and noon.

(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.

(3) If any question on the exercise lists is not clear enough, please feel free to contact joao.sobral@itp3.uni-stuttgart.de 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).

### Numerical illustrations

To visualize content of the lecture I will sometimes use Wolfram Mathematica or Matlab. 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. As a student you have free access to Matlab and you can display the Mathematica files on your computer using the Wolfram Player for Notebooks.

### Survey and feedback

Please help me improve the quality of the lecture by participating in the survey I will set up on ILIAS after a few weeks of lectures. Moreover, please ask questions if something is unclear or if I assume you already know something but were never taught.

### Problem Sets

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

1 | 18.10.23 | 24.10.23 | ||

2 | 26.10.23 | 31.10.23 | ||

3 | 02.11.23 | 07.11.23 | ||

4 | 09.11.23 | 15.11.23 | ||

5 | 15.11.23 | 22.11.23 | ||

6 | 22.11.23 | 29.11.23 | ||

7 | 29.11.23 | 06.12.23 | ||

8 | 04.12.23 | 13.12.23 | ||

9 | 12.12.23 | 20.12.23 | ||

10 | 02.01.24 | 10.01.24 | ||

11 | 10.01.24 | 17.01.24 | ||

12 | 16.01.24 | 24.01.24 | ||

13 | 24.01.24 | 31.01.24 | ||

14 | 28.01.24 | 07.02.24 | Final list. Klein paradox exercise is optional. |

### Tutorials

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

João Sobral and Sayan Banerjee | V57.2.326 | Friday | 08:00 |

V57.6.331 | Thursday | 14:00 |