Advanced Quantum Mechanics

• Describe the foundational concepts of quantum mechanics; the superposition principle, the quantum uncertainty relation, the probability amplitudes and entanglement.
• Describe the following mathematical concepts: Hilbert space, self-adjoint and unitary operators, orthogonal projections, composite systems and the spectral theorem.
• Explain the properties of mixed and pure quantum states and calculate measurable quantities using these states.
• Describe and discuss the structure of a quantum experiment in terms of a preparation, a manipulation and a measurement process.
• Define and apply symmetries and group theory (irreducible representations and character tables) in quantum mechanics for analysis of quantum states and classification of energy spectra.
• Discuss orbital and spin angular momentum and exploit these concepts in physical systems.
• Apply stationary and time-dependent perturbation theory.
• Explain the consequences of the indistinguishability principle of quantum particles.
• Describe the relation between bosons, fermions and the symmetries of the wave function, and the concept of a Slater determinant.
• Define the second quantized form of one- and two-particle operators and apply Wick’s theorem.
• Describe the principles behind Density Functional Theory.
• Discuss and perform calculations on modern applications of quantum mechanics in for example condensed matter physics.

States and state operators, mixtures and the density matrix, group theory and symmetries, angular moments, spin, measurement, atom-field interaction, entanglement, charged particle in magnetic field, Aharonov-Bohm effect, Zeeman effect, group theory (representations and characters), identical particles, Pauli principle, second quantisation, electronic structure theory, exhange, Hartree-Fock method, density functional theory, Hohenberg-Kohn theorems. Greens functions, superconductivity. Selected topics within modern quantum physics.

10102/10104/10303, Or corresponding courses.

Lectures, problem solving, projects.