Quantum Mechanics II

Approximation methods in quantum mechanics. Scattering theory. Atoms and electrons in magnetic fields. Coherent states. Density matrix and entanglement. Field quantization and radiation theory. Measurement and interpretation. Introduction to electron bands in solids.

KNOWLEDGE | The candidate should have knowledge about:

• Fundamental concepts and the mathematical formalism used in the general formulation of quantum mechanics (QM)
• Different types of approximation methods used in QM and which of these that is suitable for a given system
• How scattering of particles can be treated in a QM fashion
• QM effects caused by a magnetic field and quantization of the magnetic field itself
• Fundamental concepts within quantum statistics and entanglement
• How periodic potentials can be used to give a simple description of the conduction properties of materials

SKILLS | The candidate should, among other things, be able to

• Compute wavefunctions and energy eigenvalues via degenerate and non-degenerate perturbation theory, both time-dependent and time-independent
• Compute the QM scattering cross section for particles scattering on potentials/other particles in a variety of situations, including low energy, high energy and for identical particles
• Compute QM phases that arise in certain physical systems and how these phases are manifested in observables
• Determine if a quantum state is pure, mixed and/or entangled and compute the density matrix of the system
• Compute Bloch-functions and band structure for a system with a simple periodic potential

GENERAL COMPETENCY | The candidate should be able to:

• Understand different principles utilized to construct approximative methods in QM
• Understand how scattering of particles can provide important information about physical interactions
• Assess the consequence of treating a magnetic field in a QM system in either a classical or quantum mechanical fashion

Lectures and calculation exercises. The course will be given in English if students on the international master program in physics are attending the course. Expected workload in the course is 225 hours.