GOALS:
By the end of the course, students will be able to:
• Contextualise quantum theory: Contrast the limitations of classical
physics with the experimental evidence, such as interference and measurement-
based observations, that necessitate a quantum description of nature.
• Manipulate quantum states: Manage quantum states in both finite-
dimensional and continuous systems, utilising superposition and probabilistic
interpretation to explain quantum effects.
• Apply mathematical formalism: Utilise Dirac notation, complex
vector spaces, and linear operators to represent and analyse physical systems.
• Implement quantum postulates: Apply the postulates of quantum
mechanics to calculate measurement probabilities, expectation values, and the
implications of non-commuting observables.
• Analyse continuous systems: Employ wave functions, Fourier
transforms, and the Dirac delta function to describe particles in position and
momentum spaces.
• Model system dynamics: Evaluate the time evolution of quantum
systems via unitary transformations and the Schrödinger equation, relating
results to classical limits.
CONTENT:
The curriculum follows a structured progression from concrete phenomena to
general theoretical frameworks:
1 Foundations: Experimental breakdown of classical physics;
interference, the double-slit experiment, and the nature of measurement.
2 Finite-dimensional systems: Introduction to state vectors and
superposition using accessible models like photon polarisation.
3 Mathematical framework: Complex vector spaces, Dirac notation,
inner products, and linear operators.
4 Observables & measurement: Hermitian operators, spectral
decomposition (eigenvalues/vectors), commutators, and Heisenberg’s uncertainty
principle.
5 Continuous degrees of freedom: Wave functions in one dimension,
probability densities, and the relationship between position and momentum
representations.
6 Quantum dynamics: Unitary time evolution, the Schrödinger
equation, and the quantum-classical correspondence principle.
EXAM:
Written exam (120 min), Registration: FlexNow
- Kursleiter/in: Serim Ilday