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FSI3045 Advanced Quantum Mechanics 7.5 credits

"Advanced Quantum Mechanics" is a basic continuation course in quantum mechanics that aim at the applications of quantum mechanics. The course should give you deeper knowledge about the foundations of quantum mechanics and skills in problem solving in quantum mechanics.

Course offering missing for current semester as well as for previous and coming semesters
Headings with content from the Course syllabus FSI3045 (Spring 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Dirac's bracket notation. Hermitian and non-Hermitian operators. Wave packets. Path integral formulation of quantum theory. Matrix formulation. Density matrices. Many-body systems. Symmetries, rotational invariance, and angular momentum. The hydrogen atom. Spin. Addition of angular momenta. The variational principle and the WKB approximation. Time independent and time dependent perturbation theory. The Aharonov-Bohm effect. Introduction to scattering theory. Møller's wave operators. The Lippmann-Schwinger equation. Scattering matrices. The Born series and the Born approximation. Scattering amplitude, differential cross-section, and total cross-section. The optical theorem. Partial wave analysis. Long range potentials. The Rutherford formula. Resonances in scattering. Decay width and the Breit-Wigner formula.

Intended learning outcomes

After completed course, the PhD student should be able to:

  • apply Dirac's bracket notation.
  • use Hermitian and non-Hermitian operators.
  • know the path integral formalism of quantum theory.
  • have knowledge about the matrix formulation of quantum mechanics and use density matrices.
  • compute angular momentum and spin as well as have a good command of addition of angular momenta.
  • use the variational principle and the WKB approximation.
  • know the Aharonov-Bohm effect.
  • have general knowledge about scattering theory as well as compute basic quantities in scattering theory.

Course disposition

No information inserted

Literature and preparations

Specific prerequisites

Mathematical Methods in Physics.
Quantum Physics.

Recommended prerequisites

No information inserted


No information inserted


R. Shankar, Principles of Quantum Mechanics, Kluwer (1994)

Övrig litteratur:

  • R.L. Liboff, Introductory Quantum Mechanics, Addison-Wesley (2003)
  • J.J. Sakurai, Modern Quantum Mechanics, Addison-Wesley (1994)

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

P, F


  • TEN1 - Written exam, 5,0 hp, betygsskala: P, F
  • TEN2 - Oral exam, 2,5 hp, betygsskala: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Other requirements for final grade

A written and oral exam.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

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Profile picture Jens Bardarson

Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web FSI3045

Offered by


Main field of study

No information inserted

Education cycle

Third cycle

Add-on studies

No information inserted


Edwin Langmann,

Postgraduate course

Postgraduate courses at SCI/Physics