Integrative teaching
Vasco Cavina
Examination procedure
<p>The final assessment will be an oral exam.</p>
Examination procedure notes
<p>The oral exam consists of a discussion of approximately 40 minutes, during which the candidate is asked to solve problems related to the material covered in the course.</p>
Prerequisites
Basic Linear Algebra
Fundamental concepts such as vector spaces, orthonormal bases, linear operators, eigenvalues, and eigenvectors.
Classical Electrodynamics
Basic principles of electric and magnetic fields, Maxwell’s equations, electromagnetic potentials, and gauge concepts.
Analytical Mechanics
Lagrangian and Hamiltonian formulations of mechanics, principle of least action, generalized coordinates, and conservation laws.
Syllabus
Mathematical Methods
Algebraic and analytical tools used in the formulation of quantum theory.
Axiomatic Introduction to the Theory
Postulates of quantum mechanics and the physical meaning of operators, observables, and states.
Temporal Evolution
Schrödinger equation, time evolution operators, Schrödinger and Heisenberg pictures.
1D Systems
Infinite square well, potential wells and barriers, harmonic oscillator.
Characteristic Function and Wigner Distribution
Phase-space formalism, quasi-probability representations of quantum states.
Magnetic Fields
Quantization in the presence of magnetic fields, magnetic moment, and gauge invariance.
Aharonov-Bohm Effect
Topological effects and the role of the vector potential in quantum mechanics.
Angular Momentum
Orbital and intrinsic angular momentum, operator algebra, quantization.
Central Potentials
Spherically symmetric problems, radial equation, hydrogen atom.
Spin
Spin-½ systems, spin operators, Stern–Gerlach experiment.
Discrete Symmetries (Parity, Time-Reversal)
Fundamental symmetries and their implications on dynamics and state structure.
Approximation Methods
Perturbation theory (non-degenerate and degenerate), WKB method.
Identical Particles
Indistinguishability principle, state symmetrization, Bose–Einstein and Fermi–Dirac statistics.
Bibliographical references
J.J. Sakurai, “Meccanica Quantistica Moderna” (Zanichelli, Bologna 1985)
L. Ballantine, “Quantum Mechnics” (World Scientific, Singapore 1998)
A. Messiah, “Quantum Mechanics” (Dover, New York 1999)