Advanced Quantum Mechanics (Quant3)

Course content

The course is a graduate level in quantum mechanics with emphasis on providing the students with tools to understand the advanced courses within the quantum branch of the master program. The introductory undergraduate quantum mechanics curriculum is reviewed and expanded with emphasis on important concepts such as symmetries, approximate methods, scattering theory, and second quantization. The course introduces the concepts of propagators and density matrices, applied to physical examples, as well as relativistic quantum mechanics.



MSc Programme in Physics
MSc Programme in Physics with a minor subject

Learning outcome


The course gives knowledge about the modern quantum mechanics formalism, including Dirac notation, density matrices, different representations (such as e.g. position and momentum representations), and the importance of symmetries for conservation laws and practical solutions of quantum mechanical problems. Furthermore, the principles of scattering theory and time-dependent perturbation theory is an important part of the course, as well as introductions to relativistic and many-particle states.

The course should provide the student with the ability to:

  • Understand a quantum mechanical description of physical systems.
  • Solve  both time-dependent and time-independent
    simple examples of quantum mechanical problems using the Dirac formalism.
  • Use the concept of propagators and understand Feynman's method of path integrals.
  • Use symmetry arguments to simplify the c.alculations and to understand the corresponding conserved quantities
  • Calculate scattering amplitudes using advanced scattering theory
  • Formulate and perform calculations on many-body problems in terms of second quantization.
  • Understand the relativistic Dirac equation and its relation to non-relativistic quantum mechanics.


This course will provide the students with the necessary background for further studies in the different topics of quantum physics, such as quantum optics, condensed matter physics and particle physics, and it will give the student some of the necessary tools needed for analyzing physical systems where quantum mechanical effects play an important role. Students will also be introduced to simple quantum computations that allow us to illustrate and probe the behavior of quantum systems.

Lectures and exercise sessions

See Absalon for final course material. The following is an example of expected course literature.


J.J. Sakurai and Jim Napolitana, Modern Quantum Mechanics.

10-15 ECTS undergraduate courses in quantum mechanics

Academic qualifications equivalent to a BSc degree is recommended.

7,5 ECTS
Type of assessment
Written examination, 4 hours under invigilation
Continuous assessment
Type of assessment details
The exam consists of two parts; the required homework sets count for 50% of the final grade. The 4 hours written exam without aids counts for 50% of the final grade.
Without aids

For the homework sets, all aids are allowed. For the written exam, no aids are allowed.

Marking scale
7-point grading scale
Censorship form
No external censorship
course responsible plus one censor.

Same as ordinary written 4 hour exam. Points from finished homeworks sets during the course count for 40% of the grade. The homework sets cannot be resubmitted.

If there are 10 students or less signed up for the re-exam, the exam will be changed to oral examination.

Criteria for exam assessment

see learning outcome

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 90
  • Theory exercises
  • 42
  • Project work
  • 42
  • Exam
  • 4
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

Block 1
no limit
The number of seats may be reduced in the late registration period
Study Board of Physics, Chemistry and Nanoscience
Contracting department
  • The Niels Bohr Institute
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Markus Tobias Ahlers   (13-55697a737d7b366970746d7a7b48766a7136737d366c73)

Markus Tobias Ahlers

Saved on the 12-06-2023

Are you BA- or KA-student?

Are you bachelor- or kandidat-student, then find the course in the course catalog for students:

Courseinformation of students