
Course unit
PRINCIPLES OF THEORETICAL PHYSICS
SCP4065497, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2016/17
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
FIS/02 
Theoretical Physics, Mathematical Models and Methods 
14.0 
Course unit organization
Period 
First semester 
Year 
3rd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
5.0 
40 
85.0 
No turn 
Lecture 
9.0 
72 
153.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
3 Istituzioni di Fisica Teorica 
01/10/2018 
30/11/2019 
MARCHETTI
PIERALBERTO
(Presidente)
STELLA
ATTILIO
(Membro Effettivo)
BALDOVIN
FULVIO
(Supplente)

2 Istituzioni di Fisica Teorica 
01/10/2017 
30/11/2018 
FERUGLIO
FERRUCCIO
(Presidente)
STELLA
ATTILIO
(Membro Effettivo)
BALDOVIN
FULVIO
(Supplente)
MARCHETTI
PIERALBERTO
(Supplente)

Prerequisites:

Students should know phenomenological elementary aspects of quantum mechanics and they should possess a basic knowledge of Hilbert spaces and operators defined on them. Furthermore some knowledge of equilibrim thermodynamics and hamiltonian classical mechanics is required. 
Target skills and knowledge:

The aim of the course is to give the conceptual and formal basis of quantum mechanics and to propose some applications to elementary systems. Furthermore it introduces to equilibrium statistical mechanics based upon ensemble, both classical and quantum, with applications to noninteracting systems. 
Examination methods:

Written and oral examinations for the part concerning quantum mechanics, only wriiten examination for the part concerning statistical mechanics. 
Assessment criteria:

To evaluate the understanding of the theoretical concepts and to check the ability of solving exercises related to the topics of the course. 
Course unit contents:

QUANTUM MECHANICS
The formalism of Quantum Mechanics and its physical interpretation: wavefunctions, Hilbert spaces, basis, states; observables, selfadjoint operators; spectrum, eigenvalues and eigenvectors, spectral family; Dirac's formalism; causal time evolution for conservative systems, stone theorem; preparation of states and measures, von Neumann's projection postulate.
General consequences of the postulates, the Heisenberg uncertainty principle, complete sets of compatible observables; composite systems.
Solution of the Schroedinger equation for conservative systems: series expansion in energy eigenstates; wells and potential barriers in onedimensional systems; the harmonic oscillator in 1d, creation and annihilation operators, spectrum and eigenfunctions of the Hamiltonian; free particle in 3d.
Angular momenta: commutation relations, spectrum, orbital angular momenta and spherical harmonics, composition of angular momenta, spin.
Particles in central potential: radial equation, quantum numbers; hydrogen atom, spectrum and eigenfunctions of the Hamiltonian.
Identitical particles: symmetrization postulate and Pauli principle.
Scattering theory
Timeindependent perturbation theory
Brief mention to mixed states, EPR, the Bell inequalities and interpretative issues.
STATISTICAL MECHANICS
 MaxwellBoltzmann distribution for the ideal gas, microstates and macrostastes.
Classical statistical ensembles.
Entropy, temperature, free energies, thermodynamic limit and extensivity, fluctuations, classical equipartition.
Quantum states of fermions and bosons, density matrix, quantum ensembles, boson and fermion gas in the grandcanonical ensemble.
BoseEinstein condensation, properties of degenerate Fermi gas, classical limit of the quantum statistics. 
Planned learning activities and teaching methods:

Lectures of theory and exercices. 
Textbooks (and optional supplementary readings) 

Claude CohenTannoudji, Bernard Dui, Frank Laloe, Quantum Mechanics, Vol I. : 1992 Wiley Interscience, .

Konishi, Kenichi; Paffuti, Giampiero, Meccanica quantistica: nuova introduzione. Pisa: PlusPisa university press, 2006.

Kerson Huang, Meccanica Statistica. : Zanichelli, 1997.


