Syllabus
Syllabus: Prerequisites for the Master program in Physics in Rome Sapienza
CLASSICAL MECHANICS
Some general concepts of analytical mechanics as presented in undergraduate textbooks. In the
following we will refer to the undergraduate textbook:
H. Goldstein, C. P. Poole, and J. L. Safko, Classical Mechanics, Addison-Wesley (GPS)
Topics:
a) Survey of elementary principles: mechanics of a particle, mechanics of a system of particles,
constraints, D’Alembert’s principle and Lagrange’s equations (Chapt. 1 of GPS)
b) Oscillations: formulation of the problem, the eigenvalue equation and the principal axis
transformation, frequencies of free vibration and normal coordinates (Chapt. 6 of GPS)
c) The Hamilton equations of motion and the Legendre transformations (Chapt. 8 of GPS)
d) Canonical transformations, Poisson brackets and Liouville’s theorem (Chapt. 9 of GPS)
CLASSICAL ELECTROMAGNETISM
Some general concepts of electromagnetism as presented in undergraduate textbooks. In the
following we will refer to the undergraduate textbook:
D. Halliday, R. Resnick, and K. S. Crane, Physics - part II, John Wiley & Sons (HRC)
Topics:
a) Electric charge and Coulomb’s law: electric charge, conductors and insulators, Coulomb’s law,
continuous charge distributions, conservation of charge (Chapt. 25 of HRC)
b) The electric field of point charges and charge distributions (Chapt. 26 of HRC)
c) The flux of the electric field and Gauss’ law (Chapt. 27 of HRC)
d) Electric potential energy and potential: definitions, determination of the potential from the field
and viceversa, potential of point charges and charge distributions, equipotential surfaces, the
potential of a charged conductor (Chapt. 28 of HRC)
e) The electric properties of materials: conductors and insulators in an electric field, Ohm’s law and
ohmic materials (Chapt. 29 of HRC)
f) Capacitance and capacitors (Chapt. 30 of HRC)
g) DC circuits: electric current and electromotive force (Chapt. 31 of HRC)
h) The magnetic field: the magnetic force on a moving charge, circulating charges, the Hall effect
(Chapt. 32 of HRC)
QUANTUM MECHANICS
Some general concepts of quantum mechanics as presented in undergraduate textbooks. In the
following we will refer to the undergraduate textbook:
J. J. Sakurai, Modern Quantum Mechanics, Addison-Wesley (Sak)
Topics:
a) Fundamental concepts: kets, bras, operators, Hilbert space, basis, matrix representation,
measurements, observables, and uncertainty relations, position, momentum, and translation,
wave functions in position and momentum space (Chapt. 1 of Sak)
b) Quantum dynamics: time evolution, Schroedinger equation, Schroedinger and Heisenberg
representation, harmonic oscillator, finite-depth and infinite-depth square well (Chapt. 2 of Sak)
c) Theory of angular momentum: rotations and angular momentum commutation relations, spin 1/2
systems and finite rotations, eigenvalues and eigenstates of angular momentum, orbital angular
momentum, addition of angular momenta and Clebsch-Gordan coefficients (Chapt. 3 of Sak)
d) Symmetry in quantum mechanics: symmetries, conservation laws, degeneracies. Discrete
symmetries, parity (space inversion). Lattice translations as a discrete symmetry. The time-reversal
discrete symmetry (Chap. 4 of Sak)
e) Approximation methods. Time-independent perturbation theory (degenerate and nondegenerate
case). Time-dependent perturbation theory (Chap. 5 of Sak).
STATISTICAL MECHANICS
Some general concepts of classical and quantum statistical mechanics as presented in undergraduate
textbooks. In the following we will refer to the undergraduate textbook:
K. Huang, Statistical Mechanics, John Wiley & Sons (Hua)
Topics:
a) Classical statistical mechanics: the postulate of classical statistical mechanics, microcanonical
ensemble, derivation of thermodynamics, equipartition theorem, classical ideal gas (Chapt. 6 of
Hua)
b) Canonical and grand canonical ensemble. Energy fluctuations in the canonical ensemble and
density fluctuations in the grand canonical ensemble, the chemical potential; equivalence of the
canonical and the grand canonical ensemble (Chapt. 7 of Hua)
c) Quantum statistical mechanics. The postulate of quantum statistical mechanics, ensembles in
quantum statistical mechanics. Ideal gas: microcanonical and grand-canonical ensemble (Chapt. 8
of Hua) (Chapt. 8 of Hua)
d) Fermi systems: the equation of state of an ideal Fermi gas (Chapt. 11 of Hua)
e) Bose systems: photons and Planck distribution, Bose-Einstein condensation (Chapt. 12 of Hua)
ATOMIC AND MOLECULAR PHYSICS
Some general concepts of atomic and molecular physics as presented in undergraduate textbooks. In
the following we will refer to the undergraduate textbook:
B. H Bransden & C. J. Joachain, Physics of atoms and molecules, Longman Scientific & Technical
(BJ)
Topics:
a) One-electron atoms: the Schroedinger equation for one-electron atoms, energy levels. the
eigenfunctions of the bound states (Chapt. 5 of BJ)
b) Two-electron atoms: the Schroedinger equation for two-electron atoms, spin-wave functions and
the role of the Pauli exclusion principle; level scheme of two-electron atoms (Chapt. 6 of BJ)
c) Many-electron atoms: the central field approximation, the periodic system of the elements
(Chapt. 7 of BJ)
d) Molecular structure: the general nature of the molecular structure, the Born-Oppenheimer
separation for diatomic molecules, electronic structure of diatomic molecules, the structure of
polyatomic molecules (Chapt. 9 of BJ)
NUCLEAR AND SUBNUCLEAR PHYSICS
Some general concepts of nuclear and subnuclear physics as presented in undergraduate textbooks.
Topics:
· Atomic physics: Discovery of nucleus and nucleons.
· Nuclear physics: nucleus properties and nuclear models
· Radioactivity: Alfa, beta and gamma decays
· Relativistic kinematics. Scattering. Cross section and decay branching fraction
· Interaction of particles with matter
· Particle detectors and accelerators
· Invariance principles and conservation laws: parity, charge conjugation, time reversal
· Spin and helicity
· Isospin
· Quark model and hadronic resonances
· Leptons, hadrons and elementary families of matter
· Fundamental interactions of particles: weak, electromagnetic and strong interactions.
· Particles and antiparticles: CP symmetry
· Neutrino oscillation
The material can be found in:
1. Donald H. Perkins, Introduction to High Energy physics, 4th edition
(https://doi.org/10.1017/CBO9780511809040 )
2. Carlos A. Bertulani, Nuclear Physics in a Nutshell
(https://press.princeton.edu/titles/8455.html )
3. R. Cahn and G. Goldhaber, The experimental foundations of Particle Physics,
(https://doi.org/10.1017/CBO9780511609923 )
4. William R. Leo, Techniques for Nuclear and Particle Physics Experiments
(https://www.springer.com/us/book/9783540572800 )
5. David Griffiths, Introduction to Elementary Particles
(https://www.wiley.com/en-us/Introduction+to+Elementary+Particles+%2C+2nd
%2C+Revised+Edition-p-9783527406012 )
COMPUTING METHODS
The student should have some knowledge of the C programming language and of the Unix
environment. In particular he should be acquainted with concepts like: Flow diagrams, conditions
and If statements, for and while loops, arrays, pointers, functions, file input/output.
Moreover, he should be able to use simple numerical methods for integration, like the Euler and the
Monte Carlo method, and for the solution of simple differential equations.
As an introduction to C and a review of the basic concepts, one can use any book on C
Programming or one of the many free web resources available online, e.g.:
https://www.learn-c.org
https://www.coursera.org/specializations/c-programming
Numerical methods are presented in, e.g., Numerical Recipes in C: The Art of Scientific
Computing, by B. P. Flannery, S. Teukolsky, W. H. Press, and W. T. Vetterling
English
Italiano
