(Created 2011-09-01.)

QUANTUM MECHANICS, ADVANCED COURSE 2 | FMFN10 |

**Aim**

The course should give the student an ability to perform calculations and derivations using a modern quantum mechanical formalism, especially in vector spaces with continuous eigenvalue spectra. The student should also achieve an improved ability to assimilate the contents of research articles in modern physics and be able to apply the formalism on concrete physical problems.

*Knowledge and understanding*

For a passing grade the student must

- have a knowledge and understanding of the basic foundations of modern quantum mechanics
- understand the possibilities and limitations of quantum mechanics
- be able to choose and carry through a quantum mechanical analysis to solve or illuminate some physical question

**Contents**

- Fundamental concepts and quantum dynamics.
- Theory of Angular momemtum, the groups SO(3) and SU(2), Euler rotations, representations of the rotation operator, addition of angular momenta, Bell's inequality, tensor operators, Wigner-Eckart theorem.
- Symmetries in quantum mechanics: Parity, lattice translations, time-reversal.
- Approximation methods: Interaction picture, time-dependent perturbation theory.
- Many-particle theory and second quantization: identical particles, bosons, fermions, field operators.
- Scattering theory: Lippmann-Schwinger equation, Born approximation, optical theorem, partial waves.

**Literature**

Sakurai, J.J., Modern Quantum Mechanics,Addison-Wesley Publ. Company, 1994, ISBN: 0-201-53929-2