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.
FSI3045 Advanced Quantum Mechanics 7.5 credits

Information per course offering
Information for Autumn 2024 Start 26 Aug 2024 programme students
- Course location
AlbaNova
- Duration
- 26 Aug 2024 - 27 Oct 2024
- Periods
- P1 (7.5 hp)
- Pace of study
50%
- Application code
50970
- Form of study
Normal Daytime
- Language of instruction
English
- Course memo
- Course memo is not published
- Number of places
Places are not limited
- Target group
- No information inserted
- Planned modular schedule
- [object Object]
- Schedule
- Schedule is not published
- Part of programme
- No information inserted
Contact
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus FSI3045 (Spring 2019–)Headings with content from the Course syllabus FSI3045 (Spring 2019–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
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.
Literature and preparations
Specific prerequisites
Mathematical Methods in Physics.
Quantum Physics.
Literature
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
Examination
- TEN1 - Written exam, 5.0 credits, grading scale: P, F
- TEN2 - Oral exam, 2.5 credits, grading scale: 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.
Examiner
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 room in Canvas
Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.
Offered by
Main field of study
This course does not belong to any Main field of study.
Education cycle
Third cycle