General Prerequisites
Mathematics:
Differential & Integral Calculus
Differential Equations
Linear Algebra (e.g., eigenvalues, matrices)
Complex Numbers
Physics:
Classical Mechanics
Wave Physics & Optics
Introduction to Modern Physics (e.g., particle-wave duality, Heisenberg uncertainty principle, energy quantization, double-slit experiment, Bohr model of the atom)
Learning Outcomes
- Handle the mathematical structure of Quantum Mechanics using operators, eigenvalues, and eigenstates.
- Solve one-dimensional and three-dimensional quantum problems using the Schrödinger equation.
- Apply the theory of angular momentum and spin, including the addition of angular momenta.
- Develops and applies the time-independent non-degenerate perturbation theory.
- Interpret physical results and measurable quantities based on the probabilistic nature of Quantum Mechanics.
Course Content (Syllabus)
- The principle of wave–particle duality as the fundamental law of quantum mechanics. Schrödinger equation.
- The statistical interpretation of the Schrödinger equation.
- Linear operators.
- Compatible physical observables, properties of commutators.
- The uncertainty principle.
- Simple quantum systems: rectangular wells, potential barriers, tunneling effect, harmonic oscillator, etc.
- Three-dimensional problems: particle-in-a-box quantization, three-dimensional harmonic oscillator
- Central potentials, hydrogen atom
- Angular momentum and spin
- Identical particles, bosons and fermions
- Time-independent non-degenerate perturbation theory
Course Bibliography (Eudoxus)
- Κβαντική Μηχανική, Zetilli Ν., Εκδόσεις Σοφία, 2025 (Εύδοξος: 122090349)
- Κβαντική Φυσική, Gasiorowicz S., Εκδόσεις Κλειδάριθμος, 2015 (Εύδοξος: 50656332)