Course syllabus for Quantum physics

Linear algebra, multivariable analysis and mechanics.

The aim of this course is that participants should become familiar with the fundamental principles of quantum mechanics. Participants will acquire the mathematical and conceptual tools needed to describe physical systems quantum-mechanically, and then apply these tools to generate predictions of practically relevant quantum-mechanical phenomena. It also aims to bring out the connections between quantum-mechanical concepts and classical physics, chemistry, and technological applications. The emphasis is on problem solving.

1. Describe quantum-mechanical systems using quantum states, wavefunctions and probability amplitudes.
2. Predict particle motion in one-dimensional and three-dimensional (spherically symmetric) potentials, including the "particle in a box", the harmonic oscillator, and the hydrogen atom.
3. Explain quantum-mechanical phenomena in terms of wavefunction collapse, interference and the uncertainty and exclusion principles.
4. Account for how quantum-mechanical methods are applied in chemistry and technology.

1. Experimental background: why do we need quantum mechanics?
2. Probability and probability amplitudes
3. States and wavefunctions
4. Position and momentum operators, the Hamiltonian
5. Measurement and expectation values
6. Time-independent and time-dependent Schrödinger equations
7. Free particles
8. One-dimensional potentials: bound states, scattering and tunnelling
9. The harmonic oscillator
10. Perturbation theory
11. Rotations, angular momentum and spin
12. The hydrogen atom (gross and fine structure)
13. Multiparticle systems
14. Atoms and molecules
15. Quantum computing

Lectures and problem sessions. One laboratory assignment, at a chosen time during course.

1. Hand-in problems (20% x 3)
2. Laboratory session
3. Written exam (40%)

In order to pass the course (grade 3), the student must obtain at least 40 % of the total points in the hand-in problems, at least 40 % of the total points in the exam, and have completed the laboratory assignment. Higher grades require, in addition to the above, that the combined score from the hand-in problems and the exam, weighted by 60 % and 40 % respectively, exceeds 60 % for grade 4or 80 % for grade 5.