Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Advanced Quantum Mechanics (Quant3)

Practical information
Study year 2016/2017
Block 1
Programme level Full Degree Master
Course responsible
  • Karsten Flensberg (9-6d736c757a696c796e4775697035727c356b72)
  • The Niels Bohr Institute
Course number: NFYK15003U

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.


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.

Recommended prerequisites

10-15 ECTS undergraduate courses in quantum mechanics


mandatory course for specialisation "Quantum physics". Restricted elective course for specialisation "Physics".

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MSc Programme in Physics


Study Board of Physics, Chemistry and Nanoscience

Course type

Single subject courses (day)


1 block


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Teaching and learning methods

Lectures and exercise sessions


no limit




The course is based on the text book: J.J. Sakurai and Jim Napolitana, Modern Quantum Mechanics, 2nd edition (international edition).


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


Type of assessment

Written examination, 4 hours under invigilation
Continuous assessment
The exam consists of two parts; the required homework sets count for 40% of the final grade. The 4 hours written exam counts for 60% of the final grade.


Only certain aids allowed

Book and notes are allowed, but no computer or calculator.

Marking scale

7-point grading scale

Criteria for exam assessment

The highest mark (12) is given for excellent exam performance that demonstrates full mastering of the above mentioned teaching goals under Skills with no or only small irrelevant gaps. The grade 2 is given to a student who has achieved only minimally the course goals descirbed under Skills.

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.
For the third exam attempt, the student may choose to follow the course again and take the regular exam, or take the re-exam.
If there are 10 students or less signed up for the re-exam, the exam may be changed to oral examination.

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