Quantum Mechanics II

Module PH7014

This module is offered by Ludwig-Maximilians University Munich (LMU). It is available for TUM students only within a joint degree program (e. g. M. Sc. Quantum Science & Technology).

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

PH7014 is a semester module in English or German language at which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

Focus Area Theoretical Quantum Science & Technology in M.Sc. Quantum Science & Technology

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workload	Contact hours	Credits (ECTS)
270 h	120 h	9 CP

Responsible coordinator of the module PH7014 is Ivo Sachs.

Content, Learning Outcome and Preconditions

Content

This module provides a second course on quantum mechanics, which is a recommended prerequisite for any future courses such as many-body physics and field theory in all areas of physics. The contents of this module vary somewhat from year to year, depending on the preferences of the lecturer; interested students are advised to contact the lecturer in advance for details. A typical lecture course on Quantum Mechanics II starts with a chapter recapitulating the material of Quantum Mechanics I, namely the basic postulates, the density matrix formalism, path integrals, angular momentum, perturbation theory. The next chapter provides a brief introduction to concepts of quantum information theory, such as entanglement and the role it plays in the Bell inequalities. A brief chapter on topological concepts, such as the Aharonov-Bohm phase, Berry phase, and Landau levels could follow. The course proceeds with a chapter on the quantization of the electromagnetic field, a discussion of light-matter interactions, and the derivation of selection rules based on symmetry arguments. This is followed by chapters on time-dependent perturbation theory and on scattering theory, including concepts as the Born approximation, Lippmann-Schwinger equation, T-matrix etc. The course includes a chapter on relativistic quantum mechanics, discussing the Klein-Gordon and Dirac equations and its consequences, such as spin-orbit coupling and fine structure with possible excursions to the graphene dispersion and Klein tunneling. The final chapter covers the formalism of second quantization and simple applications such as solving tight-binding models and the role of statistics.

Learning Outcome

After successful completion of the module the students are able to:

Has a solid basis to undertake studies in many-body physics, field theory, particle physics, solid-state physics, cold atomic physics, quantum optics etc.
Is familiar with coupling quantum particles to gauge potentials
Is able to solve single particle scattering problems
Understands relativistic quantum mechanics, the difference between positive and negative energy states, and can recognize the Dirac equation as an effective Hamiltonians
Has a working knowledge of second quantization

Preconditions

No prerequisites in addition to the requirements for the Master’s program in Quantum Science and Technology. Familiarity with quantum mechanics is assumed, at the level of an introductory course from a Bachelor degree in physics.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

WS 2022/3 WS 2021/2 WS 2020/1

Type	SWS	Title	Lecturer(s)	Dates	Links
VO	4.0	T_M2: Fortgeschrittene Theoretische Physik (Quantum Mechanics II)	Khaldieh, M. Hell, A. Mukhanov, V. Creswell, J.	see LSF at LMU Munich	current
UE	2.0	Übungen zu T_M2: Fortgeschrittene Theoretische Physik (Quantum Mechanics II)	Creswell, J. Hell, A. Mukhanov, V. Khaldieh, M.	see LSF at LMU Munich	current
UE	2.0	Zentralübungen zu T_M2: Fortgeschrittene Theoretische Physik (Quantum Mechanics II)	Hell, A. Mukhanov, V. Khaldieh, M. Creswell, J.	see LSF at LMU Munich	current

Learning and Teaching Methods

The module consists of a lecture series (4 SWS), exercise classes (2 SWS), comprising two lecture sessions and one exercise session per week. The main teaching material is presented on the blackboard or by beamer. Lectures are supplemented by weekly problem sets, deepening the understanding of core concepts through concrete calculations. Solutions to the problem sets are discussed in the exercise sessions. Participation in the exercise classes is strongly recommended, since the exercises are aids for acquiring a deeper understanding of the core tools of condensed matter many-body physics and field theory and for practicing to solve typical exam problems.

Media

Power point and Keynote presentations, blackboard.

Literature

Standard textbooks on quantum mechanics, e.g.:

R. Shankar, Principles of Quantum Mechanics
G. Baym, Lectures on Quantum Mechanics
E. Merzbacher, Quantum Mechanics
J. Sakurai, Quantum Mechanics
C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics Vol 1 and 2
L. E. Ballentine, Quantum Mechanics
D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics (3rd Ed.)

Module Exam

Description of exams and course work

There will be a written exam of 180 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using conceptual questions and computational tasks.

For example an assignment in the exam might be:

Find the energy eigenstates for a particle in a 2D plane subject to a perpendicular magnetic field.
Compute the scattering amplitude for a symmetric square well potential.
Solve the Dirac equation for a relativistic particle incident on a step potential.
Solve a tight-binding model such as obtaining the dispersion of graphene.

Exam Repetition

The exam may be repeated at the end of the semester.