Learning objectives
By means of frontal lessons, the student acquires the
methods and knowledges required to describe elementary
physical systems using the theory of Quantum Mechanics.
Through practical classroom exercises connected to
some important topics, students learn how to
apply the acquired knowledge using mathematical calculus.
Prerequisites
Classical Mechanics and Electromagnetism, Mathematical methods of Physics, Analytical Mechanics.
Course unit content
The course aims to provide students with the general elements of Quantum Mechanics. Therefore,the first part of the course deals with the physical effects and the experiments that led to the formulation of the theory. In the second part we elaborate the theory, introducing the mathematical formalism solving some relevant physical system. in the third part the theory is applied to some problem of atomic physics.
Full programme
1) Introduzione
Black-body and UV catastrophe, Planck idea, specific heat, photoelectric effect, Bohr atom, Bohr-Sommerfeld. Compton effect and DeBroglie.
2) Quantum Mechanics
Schrodinger equation and properties, free solution, one-dimensional case. Probabilistic interpretation of wave function.
General formalism: Hilbert spaces , states, observables/operators,
probabilities, expectation values medi, complete set of observables, measures,Heisenberg relations. One-dimensional systems: well, tunnelling, transmission and reflections, scattering. Harmonic oscillator
(analytic and algebric solution). Angular orbital momentum, spherical harmonics a. Rotations and symmetries, unitary transformations. Three-dimensional systems: rotational invariance, central potentials, hydrogen atom. Introduction of magnetic field, gauge symmetry, Landau levels. General theory of angular momentum: algebraic solution, spin and sum of angular momentums. Time-independent perturbation theory: non-degenerate and degenerate cases.
Time-dependent perturbation theory: general formalism, transition amplitudes, Fermi golden rules.
3) Application to atomic physics.
Variazional method and applications. Spin-statistics, Pauli principle, bosons e fermions, applications to multi-electron atoms, helium atom. Atoms in magnetic field: Zeeman effetcs, transitions. Fine structure: relativistic corrections, spin-orbit etc.. Comparison with exact Dirac solution. Hyperfine structure. Self-consistent methods: Hartree-Fock and generalizations (general formalism).
Bibliography
Introduzione alla meccanica quantistica, D.J. Griffiths, D.F. Schroeter. Editore: Zanichelli
Meccanica quantistica moderna; Jun J. Sakurai,Jim Napolitano, Editore: Zanichelli
Teaching methods
Frontal teaching, exercises, both in class and at home.
Assessment methods and criteria
A written test based on three exercises, to be completed in three hours. An oral examination consisting of three questions, each on one of the three parts of program.
Two written partial exams will take place during the course of the lectures. Passing both of them will allow direct access to the oral examination.
Other information
2030 agenda goals for sustainable development
