# SI3045Advanced Quantum Mechanics7.5 credits

## Kvantmekanik, fortsättningskurs

"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.

Third cycle

D

• #### Grade scale

At present this course is not scheduled to be offered.

## 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.

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.

## Eligibility

Mathematical Methods in Physics.
Quantum Physics.

## Literature

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

Other literature:

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

A written exam.

## Offered by

SCI/Theoretical Physics

Edwin Langmann,

## Examiner

Edwin Langmann <langmann@kth.se>

## Version

Course plan valid from: Spring 09.