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. It introduces the use of propagators and density matrices, applied to physical examples. Relativistic quantum mechanics is also introduced.



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 example of quantum mechanical problems using the Dirac formalism.
  • Use the concept of propagators and understand the Feynman's method of path integrals
  • Use symmetry argument to simplify the calculations and to understand the conserved quantities
  • Calculate scattering amplitude using advance scattering theory
  • Formulate and do calculations on many-body problem 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.

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
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.
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
Study Board of Physics, Chemistry and Nanoscience
Contracting department
  • The Niels Bohr Institute
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Markus Tobias Ahlers   (13-5165766f797732656c706976774472666d326f7932686f)

Markus Tobias Ahlers
Cristian Vergu (

Saved on the 30-06-2021

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