Physics Department

Syllabus:

1 - Definition of cartesian product, ordered set, maps and graphs. Natural numbers and induction principle, real numbers and their axioms, intervals, supremum and infimum, density of rational numbers. Cartesian representation of two-dimensional and three-dimensional space.
2 - Real functions of one or more variables. Sum, product, quotient, composition of functions; monotonicity, inverse functions; description of elementary functions. Vector valued functions. Sequences.
3 - Euclidean norm in an n-dimensional space. Open sets and some topological concepts. Limits for real and vector valued functions; Cauchy criterion. Limits for sum, product, quotient, composition of functions. Limit of a monotone function. Comparison of functions going to zero or to infinity at the same point.
4 - Continuous functions. Continuous images of connected sets. Inverse of a continuous function. Sequential compacteness, Weierstrass theorem for global maxima and minima. Uniform continuity.
5 - The concept of differentiability. Partial and directional derivatives. Relations with continuity. Differential calculus. Critical points. Lagrange mean value theorem. Primitive of a given function. De L'Hospital rules. Taylor's formulas.
6 - Riemann integration over an n-dimensional interval. Integrability of continuous functions or monotone functions. Integrals of functions that are equal up to a set of zero measure. Integral functions, fundamental theorem and formula for integral calculus, integration by parts, integration of composite functions. Improper Riemann integral for unbounded functions and on unbounded intervals

Textbooks:
- P.Oppezzi, Lecture notes

General Physics I

Cmp.
Y (100 hours Lct. 3W and 40 hours Cla. 3W), at Department of Physics.
Assessement: Wr+ Or Cr: 15
Lecturer: A. SANTRONI, Department of Physics.

Syllabus:
1-Mechanics
Vectors. Kinematics. Relative motion. Dynamics of a particle. Work and Energy. Forces. Oscillatory motion. Dynamics of a system of particles. Collision processes. Dynamics of a rigid body. Gravitational interaction. Fluid statics and fluid motion. Elastic waves. Sound acoustics.
2-Heat and Thermodynamics
Temperature. Heat. Thermal conductivity. Heat convenction. Thermal radiation. Blackbody. Work. First law. Ideal gases and Wan der Waals gases. Second law. Entropy. Enthalpy. Helmholtz and Gibbs functions. Maxwell's equations. Clapeyron's equation. Kinetic theory of an ideal gas.

Textbooks:
- A. Santroni, Lecture notes
- C. Mencuccini and V. Silvestrini, "Fisica I", Liguori, Napoli.

Geometry I

Cmp.
Y(75 hours Lct. 3W + 75 Cla. 3W ), at the Department of Physics.
Assessment: Wr + Or. Cr: 15
Lecturer: D. AREZZO, Department of Mathematics.

Prerequisites: Basic concepts of trigonometry.

Syllabus:
a) Elements of set theory.
b) The principal numerical sets : from the set N of natural to that of complex numbers.
c) Linear spaces: Gauss-Jordan elimination for linear systems. Linear spaces. Subspaces. Dependent and independent subsets. The linear span of a subset. Basis and dimension. Direct sum. Scalar product, norm, orthogonality. Gram-Schmidt process. Orthogonal complement. Projections. Best approximations by elements of finite dimension subspaces.
d) Linear transformations and matrices : Linear transformations. Kernel and range of a linear transformation. The space Hom(V,W). Matrices associated to linear transformations. The space of matrices. Change of basis. Determinant and characteristic of a matrix. Binet's and Kronecker's theorems. Linear systems. Cramer's and Rouche-Capelli's theorems.
e) Analytic Geometry : Oriented segments and free vectors. Coordinates. Vector space structure of Rn. Lengths, angles. Scalar, vector and mixed products of vectors. Cartesian and parametric representations. Lines and planes. Conics. Recognition of the type of a conic from the equation. Canonical form of the equation of a conic. Sphere. Cylinder. Cone. Projections. Symmetries. Rotations. Classification of quadrics. Conics through 5 points, quadrics through 9 points. Pencils of lines, circles, conics, quadrics. Tangent line and osculating plane to a curve in a point.
f) Reduction of matrices to the diagonal form : Eigenvalues, eigenvectors and eigenspaces. Linear independence of vectors corresponding to distinct eigenvalues. Characteristic polynomial. Eigenvalues and eigenvectors of symmetric matrices. Diagonalization of hermitian, antihermitian and unitary matrices. Diagonalization of quadratic forms. Applications to conics and quadrics.

Textbooks:
- D. Arezzo, Appunti al corso di Geometria I per Fisica -Internal Notes
- T. Apostol, Calcolo, Vol. II: Geometria, Boringhieri
- F. Odetti, M. Raimondo, Elementi di Algebra Lineare, ECIG

Methods of Experimental Physics I

Cmp.
60 hours 3W+ 30 hours Cla. 2W
Assessment: Wr + Or ( and a practical test) Cr: 15
Lectures: R. CONTRI, R. MONGE, Department of Physics
This course represents the first introduction to physics experiments, and of course it implies a laboratory activity (groups of 2-3 students perform simple experiments, treat the data and write a report; this is done usually 12 times, for a total of about 50 hours).

Syllabus:
PHYSICAL QUANTITIES AND ERRORS
Physical quantities, units, dimensions. Conversions. Direct and indirect measurements. Systems of units. The International System. Instruments and their characteristics. Sensitivity and statistical errors. Mean value, mode, median. Variance and standard deviation. Standard error. Error propagation. Systematic errors. Diagrams. Non linear scales. Logarithmic scales. The least squares method. Linear function and regression lines. Combination of measurements.
MEASUREMENTS
Length and time measurements. Mass measurement. The gravity acceleration. Harmonic motion. The pendulum. Elasticity. Elastic constant and its measurement. Temperature measurement (calibration of a thermocouple). Specific heat measurement.
PROBABILITY
Combinatorial calculus. Definitions of probability. Total probability. Conditional probability. Discrete and continuous random variables. Probability density function. Joint probability. Correlation coefficient. Bienayme'-Tchebycheff theorem. Binomial, Poisson and interval distributions. Gauss distribution. The central limit theorem. Treatment of small samples. Student distribution.
STATISTICS
Statistical sample and population. Parametric estimation of a population. Confidence level. Maximum likelihood. Test of hypotesis. The chi square criterion. Statistical significance of experimental data.
COMPUTER PROGRAMMING
Introduction to the FORTRAN language. FORTRAN programs are written by the students and used in the analysis of the experimental data.+

Calculus II

Cmp.
Y(140 hours: 70 Lct. 3W + 70 Cla. 3W ), at the Department of Physics
Assessment: Wr + Or Cr: 12
Lecturer: L. BURLANDO, Department of Mathematics.

Prerequisites: Calculus I, Geometry

Syllabus:
Sequences and series of functions. Taylor series. Power series. Fourier series. Recalls about geometry of the euclidean n- dimensional space and about functions of several variables. Taylor's formula for functions of several variables. Existence results for global extrema of functions of several variables. Unconstrained local extrema for functions of several variables. The implicit function theorem and the local invertibility theorem. Constrained local extrema: the Lagrange multipliers rule. Integration of functions of several variables: Riemann integral, Peano-Jordan measure in the euclidean n-dimensional space, generalized Riemann integral. Integrals depending on a parameter. Parametrical curves in the euclidean n-dimensional space; the integral of a scalar field along a curve. Parametrical surfaces in the three-dimensional euclidean space; the integral of a scalar field on a surface. The integral of a vector field along a curve; Gauss-Green's formulae and the divergence theorem in two dimensions. Stokes' theorem in three dimensions and the divergence theorem in three dimensions. Vector fields admitting a potential. Ordinary differential equations and systems of ordinary differential equations: local and global existence and uniqueness theorems for the Cauchy problem, linear differential equations and systems. Resolution of linear differential equations of order n with constant coefficients and of linear differential systems of first order with constant coefficients. Resolution of some special kinds of differential equations.

General Physics II

Cmp.
Y(130 hours; 65 Lct. 3W and 65 Cla. 3W ), at the Department of Physics
Assessment:Wr + Or. Cr: 12
Lecturer: V.GRACCO, Department of Physics.

Prerequisites: General Physics I, Calculus, Vector Analysis

Syllabus:
Part I. Electrostatics in vacuum. Boundary problems. Electrostatics in dielectric materials.Integral and differential laws of electrostatics. Energy of the electrostatic field.
Part II. Steady currents in conductors. Ohm's law. The static magnetic field and Ampere's laws. Magnetic materials;paramagnetic, diamagnetic and ferromagnetic media.
Part III. Time varying currents and fields. The Faraday-Neumann induction law. Energy of the magnetic field .The displacement current. The Maxwell equations.Electromagnetic potentials
Part IV. Electromagnetic waves and their properties. Polarization states. Momentum and energy flow. Radiating systems. Wave guides and cavities.Propagation in dispersive media. Propagation in conductive media. Boundary conditions; reflection and refraction.
Part V. Interference of waves. Interferometric techniques in physics. Diffraction phenomena; Helmoltz-Kirchhoff diffraction theory. Light propagation in anysotropic media. Geometrical
Optics. The eikonal equation. Geometry of ray propagation; simple optical systems. Resolution limits of optical systems.

Textbooks:
- R.Feynmann, The Feynmann Lectures in Physics Vol I,II.
- A.Bobbio & G.Gatti, Elettromagnetismo
- E.Amaldi & M.Bizzarri & R.Pizzella, Fisica Generale

Theoretical Mechanics
Cmp.
Y(144 hours, 72 Lct. 3W + 72 Cla. 3W), at the Department of Physics
Assessment: Wr (3 hours) + Or (about 30 minutes) Cr: 12
Lecturer: E. MASSA, Department of Mathematics

Prerequisites: General Physics I, Calculus I, Geometry I

Syllabus:

Geometrical Preliminaries: vector spaces, linear maps, orthogonal transformations, differential geometry of curves in eucledian space.Relative Kinematics; Newton's 2nd law; elementary work and linear differential forms; vector fieldsand potential theory; constraints;Coulomb 's laws of friction.
Material systems: mass center, mechanical quantities; momentum and angular momentum balance; energy balance.
Rigid bodies: inertia tensor, mechanical quantities; Euler's equations; energy balance.
Lagrangian Mechanics: holomic constrints, configuration space-time; velocity space; d'Alembert's principle, Lagrange equations; conservation laws; equilibrium configurations, stability; small oscillations.
Hamiltonian Mechanics: phase space, Legendre transformation, Hamilton equations; simpletic structures, Poisson brackets, canonical transformations; Hamilton-Jacobi theory
Special relativity: sperimental basis, Einstein's relativity principle; Lorentz transformations; Relativistic Kinematics; point particle Dynamics.
Minkowsky space-time. Four-dimensional formulation of the Theory of Relativity

Textbooks:
- Notes by the lecturer.
- Cercignani C.,Spazio, Tempo, Movimento, Zanichelli, Bologna
- Goldstein H., Meccanica Classica, Boringhieri.
- Fasano-Marmi, Meccanica Razionale, Boringhieri.

Chemistry ( with Lab. practices)
Cmp.
Y( ), at the Department of Physics
Assessment: Cr: 12
Lecturer: A.BORSESE

Methods of Experimental Physics II
Cmp.
Y (60 Lct. 3W + 20 Cla. 1W + 14 Lab.), at the Department of Physics.
Assessment: Or + 2 Practical tests Cr: 12
Lecturers: R. EGGENHOFFNER, G.GEMME, P.MORETTINI ,Department of Physics.

Prerequisites: none (however General Physics, and Methods of Experimental Physics are highly advised)

Syllabus:

Part I Analysis of linear circuits
Systems of units, charge, current, voltage, power. Useful techniques of circuits analysis, Ohm's and Kirhhoff's laws, Thevenin and Norton's Theorems. Response of linear circuits to sinusoidal and unit step excitations. Frequency response and Fourier analysis.

Part II Semiconductor devices

Introduction of the physics of semiconducting devices. Properties of the p-n junction, diodes, BJT transistors and operational amplifiers. Polarisation of the transistors and operational amplifiers. Feedback and stability, ocillators, comparators, signal generators. Tranducers, sensors and measurements systems.

Part III Elements of combinational logic

Asyncronous digital systems. Integer number rapresentation. Sequential logic. Structure of a microprocessor system

Part IV Advances in programming techniques

Programming in Fortran and C. Analysis of the structure of programs. Techniques of experimental data analysis.

Textbooks:
- W.H.Hayt and J.E.Kemmerly, Engineering Circuit Analysis, Mc Graw Hill, 1993
- Millman-Halkias, Microelectronics, Mc Graw Hill, 1987

Mathematical Methods of Physics-A
Cmp.
Y, (Lct. 3W + Cla. 2W), at the Department of Physics
Assessment: Wr (3h) + (1h) Or. Cr: 13
Lecturer: G. VIANO, Department of Physics.

Prerequisites: Calculus I and II, Geometry I.

Syllabus:
The Theory of Functions of a Complex Variable ( 15 Lct. + 15 Cla.)
-Complex numbers and operations on complex numbers. The concept of a function of a complex variable. Cauchy-Riemann equations.
-Series of Analytic Functions. Power series. Analytic Continuation. Elementary functions of a complex variable. The Riemann surface.
-The Laurent Series and isolated singular points.
-Residues and their applications. Evaluation of definite integrals by means of the residues. Logarithmic residue. The fundamental theorem of algebra.
-Conformal mapping and application.
-Analytic and harmonic functions. Dirichlet's problem. Physical applications: two dimensional electrostatic field.

Textbooks:
- A. G. Sveshnikov and A. N. Tikhonov, The theory of Functions of a Complex Variable, Mir, 1982

Partial Differential Equations of Mathematical Physics (10 Lct. + 10 Cla.)

-Partial differential equations from a physical point of view : how the simplest partial differential equations arise. Elliptic, Hyperbolic and Parabolic type; theory of characteristics.
-Laplace's equation and Poisson's equation
-The equation for a vibrating string and its solution by D'Alambert's method. String with two fixed ends. Introduction to the theory of waves.
-Heat equation. The solution of Cauchy's problem.
-Fourier's method. Separation of variables.

Textbooks:
- S. L. Sobolev, Partial Differential Equations of Mathematical Physics, Dover (New York).

Special Functions of Mathematical Physics (18 Lct. + 8 Cla.)
-Analytical theory of linear second-order ordinary differential equations. Series solution about ordinary points. Singular points.
-Hypergeometric equation. Hypergeometric Series. Analytic continuation of hypergeometric series.
-Legendre equation. First and second kind Legendre functions.
-Confluent Hypergeometric equation. Confluent Hypergeometric function and its analytic properties. Bessel's equation

Textbooks:
- V. Smirnov; Cours de Mathe'matiques Superieures, tome III - deuxième partie - (ch. V and VI), Mir (Moscow).

Mathematical Methods of Physics-B
Cmp.
Y (70 hours Lct.), at the Department of Physics
Assessment: Wr (3h) +Or (1h). Cr: 13
Lecturer: G. CASSINELLI, Department of Physics.

Prerequisites: Calculus of one and several variables- The elementary theory of linear ordinary differential equations- Complex number system and complex exponential function-Theory of finite dimensional vector spaces.

Syllabus:
Aim of the course
Presenting some basic working tools of functional analysis (L^p spaces, classical bases of L^2 spaces, Fourier analysis) and some of their applications.
Part 1
Basic theory of integration. The Lebesgue integral. Convolution and regularization. The trigonometric bases of L^2. The orthogonal polynomials; Hermite, Legendre and spherical harmonic functions. The Fourier integral on L^1 and L^2.
Part 2
This part of the course is not fixed and presents some examples of applications of the methods presented in Part 1, mostly from Quantum Mechanics.

Textbooks:
- G. Cassinelli, Lecture Notes.

Institutions of Theoretical Physics- A
Cmp.
Y (140 hours, Lct. 4W + Cla. 2W), at the Department of Physics
Assessment: Wr ( 4h ) + Or (1h) Cr: 13
Lecturers: G. PASSATORE and G. DILLON, Department of Physics

Prerequisites: General Physics I and II, Calculus I and II

Syllabus:
- Complements of classical mechanics and optics
- Early phemnomenology and the crisis of classical concepts
- Wave-Mechanics
- The general formalism of Quantum Mechanics
- Rotation operators and the angular momentum
- Spin and identical particles
- Methods of approximation and physical applications
- Scattering
- Transition Probabilities
- Density Matrix description of mixed states

Textbooks:
- A. Messia, Quantum Mechanics
- G. Landau, E. Lifchitz, Quantum Mechanics
- J. Sakurai, Modern Quantum Mechanics

Institutions of Theoretical Physics-B
Cmp.
Y(130 hours,70 Lct. 3W + 60 Cla. 3W), at the Department of Physics
Assessment : Wr (3 hours) + Or (1 hour). Cr: 13
Lecturer: K. KONISHI, Department of Physics.

Prerequisites: General Physics I and II, Calculus I and II, Theoretical Mechanics

Syllabus:
Part I
1) Brief review of classical mechanics;
2) Historical Remarks (Planck's formula, Quanta of energy, Bohr's model of atoms, de Broglie waves);
3) Principles of Quantum Mechanics (Uncertainty Principle and Principle of Superposition, Quantum States, Operators and dynamical variables, Schödinger equation);
4) Schrödinger equation and one-dimensional systems (General properties of Schrödinger equation, current density, Ehrenfest's theorem, potential wells, harmonic oscillator, potential barrier);
Part II
5) Mathematical structure of quantum mechanics (representation theory, Hilbert space, operator and matrix, unitary transformation, mixed states and density matrix);
6) Symmetries in Quantum Mechanics;
7) Angular Momentum;
8) Schrödinger Equation and three dimensional systems (spherically symmetric potentials, parity, spherical waves, hydrogen atom, potential wells);
Part III
9) Perturbation theory (static perturbation theory, degenerate perturbation theory, t-dependent perturbation and probability of transitions);
10) Semi-classical approximation (semiclassical wave functions, tunnelling effect);
11) Wave function of particles with spin;
12) Identical particles; (Bose-Einstein and Fermi-Dirac statistics, creation and annihilation operators);
Part IV
13) Atoms and nuclei (Electron configurations, variational method and He, Isospin, deuteron);
14) (Elastic) Scattering theory (partial waves, Born approximation, Coulomb scattering);
15) Bell's inequalities.

Textbooks:
- Landau-Lifshitz, Vol.3,
- Schiff, "Quantum mechanics"
- Dirac, "Principles of Quantum Mechanics",
- Tomonaga, "Quantum mechanics"; Born, "Atomic physics",
- Feynman lectures.

Methods of Experimental Physics 3
Cmp.
Y( 70 Lct 3W + 50 Lab. ), at the Department of Physics
Assessment: by performing an original experiment or short experimental exercise + Or.
Cr: 14
Lecturer: A.SIRI, Department of Physics.

Prerequisites: none (even if General Physics 1 and 2, Methods of Experimental Physics 1 and 2 are highly advised)

Syllabus:
The course aim is to introduce to modern methods in physical measurements by showing some tecniques of digital and analogic electronics, acquisition and treatment of signals.

Part I
1S (30 Lct. 3W + 30 Lab.) Cr.7
Lecturer F.FONTANELLI

a) Elements in digital electronics: starting from combinational logic (already presented in a previous course, sequential systems are introduced, some design methodologies are presented, many exemples are given. Programmables circuits. PROM, PAL, FPLA, LCA, etc.
Introduction to microprocessor systems architecture with emphasis on digital input/output and assembly programming, the Intel X86 family as an exemple.
b) Data acquisition: A/D, D/A, digitization errors, interfaces between analog and digital systems, review of basic and analog electronics ( Thevenin theorem, transistor circuits, operational amplifier, Laplace tranform method) useful for the second part of the course.

Textbooks:
- Notes of the lectures
- F.Luccio, L.Pagli, Reti logiche e calcolatore, Boringhieri
- J.Millman- A.Grabel, Microelectronics, McGraw Hill
- P.Horowitz - W. Hill, The Art of Electronics, C.U.P.

Part II
2S (40 Lct. 3W + 20 Lab.) Cr.7
Lecturer A.SIRI

a) Systems and signals in time and frequency domain: convolution and correlation; Laplace and Fourier transforms in treating modulation; communications and sampling problems. Application in experiments of noise reduction; lock-in.
b) Measurements: synthesis of analogic instruments; analogic solution for thermal, electric and magnetic measurements; elements of feedback theory. Data acquisition; A/D, D/A and GPIB. Use of commercial LABVIEW data acquisition software; examples.

Textbooks:
- Notes of the lectures
- R.W. Henry, Electronic System and Instruments, J. Wiley & sons
- P.Horowitz - W. Hill, The Art of Electronics, C.U.P.

Structure of Matter
Cmp.
Y(70 hours Lct. 3W), at the Department of Physics
Assessment: Or. Cr: 10
Lecturer: U. VALBUSA, Department of Physics.

Prerequisites: General Physics I and II, Calculus I and II

Syllabus:
Part. 1
The statistical method and ensembles. Microcanonical ensemble. Canonical ensemble. Generalised ensembles and the Gibbs entropy formula. The ideal gas. Bose-Einstein and Fermi-Dirac statistics. Slightly degenerate perfect gases. The very degenerate Fermi gas. The Bose condensation. Photon gas. Phonon gas or fluctuations of atomic positions in a cold solid. Electron in metals. Montecarlo methods in statistical mechanics.
Part.2
The periodical table of elements, the molecular bond. Simple molecules. Specific heat of diatomic molecules. The heat capacity of solids. The Einstein model. Long wavelength compressional modes. The Debye model. The normal modes. Crystal structures. The reciprocal lattice. Diffraction of X rays. Brillouin zones.Electrons in crystals. The Kronig-Penney model. Energy bands. The Fermi surface. Metals, semiconductors and insulators. Liquids and interacting gases. The structure of a fluid. The function g(r).Measurement of g(r) by diffraction. The statistical mechanics of structure. The potentialenergy. The pair potential. The approximation of pairwise additivity. Interacting gas. Cluster expansion and the dilute gas. Liquids.

Textbooks:
- D. L. Goodstein, States of Matter, Dover Press.
- D. Chandler, Introduction to Modern Statistical Mechanics, O.U.P.

Laboratory of Electronics
Opt.
Lecturer: P.OTTONELLO, Department of Physics.

Prerequisites: General Physics I and II, Calculus I and II, Laboratory of Physics I

Part I Signals and systems
1S ( 60 hours, 40 Lect. and 20 Lab) at the Department of Physics
Assessment: Or Cr 6

Syllabus:
Noise and analog signal processing. Stochastic processes: autocorrelation and power spectral density. Noise in the electronic devices: signal to noise ratio, noise figure, noise temperature, voltage and current noise density. Man-made noise:interference reduction techniques. Bandwidth-narrowing methods: signal averaging, lock-in detection, matched filtering. Analog to digital conversion. Antialiasing filter. Zero-order hold. Microprocessor architecture. Data acquisition, memory mapped I/O, handshake, DMA. Control of a VLSI FIR filtering module through a personal computer.Typical DSP architecture. DSP evaluation boards as versatile platforms for implementing modern electronic instruments (wave and event analyzers, correlators, adaptative filters,....)

Textbooks:
- Lecture notes
- A.V.Oppenheim, A.S.Willsky, "Signals and Systems", Prentice-Hall Int.,1983
- P.Ottonello, G.Vallini, Elettronica applicata, Jackson Milano,1995.

Part 2 Process control and digital filtering
2S ( 60 hours, 40 Lect. and 20 Lab) at the Department of Physics
Assessment: Or Cr 6

Syllabus:
Transfer function, block diagrams. Nyquist's and Bode's stability criteria. Phase and gain margins, correcting networks. Errors and noise rejection. Examples. Linearization. Discrete-time systems. From Laplace to Z transform;Z transform, definition and properties. System function. Digital Fourier transform; hints for the correct use of the FFT algorithms. Digital filter design; FIR and IIR filters: comparison. Use of software packages (LabWindows and LabView). implementation of continous and discrete-time control systems.

Textbooks:
- Lecture notes.
- P.Ottonello, G.Vallini, Elettronica applicata, Jackson Milano, 1995.
- G.F.Franklin, J.D.Powel, A.Emami-Naeini, Feedback control and dynamic systems,3rd edition Addison-Wesley

Biophysics
Opt.
Y (70 Lct. 3W), at the Department of Physics.
Assessment: Or. Cr: 10
Lecturer: M.BOLOGNESI, Department of Physics

Syllabus:
Part I The structure and organization of biological matter (mostly biological macromolecules)
1S ( 35 Lct.) Cr: 5

Cell and subcellular structures. Main classes of macromolecules and their function in vivo. Non-covalent interactions at molecular level. Ammino-acid and polypeptides. Protein assembly. Ramachandran plot. Secondary and tertiary structures. Motifs, domains and quaternary structure in proteins. Main protein folds. Protein synthesis.Nucleic acid structure and function. Sequence alignement methods. Molecular evolution. Structure previous methods. Examples and computer aided molecular graphics practice.
This part makes use of interactive programs displaying protein structuress on PC, for about 4 hours.

Part II The application X-ray diffraction methods to the study of protein three-dimensional structures
2S ( 35 Lct.) Cr: 5

Basic diffraction principles. X-ray generation. Synchrotron sources. Symmetry and space groups. Fundamental properties of crystal lattices. Laue equations, scattering vector, lattice planes, Bragg equation, Ewald sphere. The reciprocal space. Structure factor and its properties; phases. The Patterson function. The isomorphous replacement data and phasing. The molecular replacement method. Crystallographic refinement. Restrained refinement. Application of molecular dynamics techniques. Reliability of crystallographic macromolecular structures. Test cases.Growth of bio- macromolecular crystals. Database for structural biology. Bio- crystallographic test calculations will be conducted and examined according to the student request.

Textbooks:
- Lecture notes.
- C.Branden,J.Tooze. Introduction to Protein Structure. Garland Publ.Co.(1991).
- M.Bolognesi et al. Introduzione alla Cristallografia Moderna, Laterza (1985).

Complements of General Physics
Opt.
Y (80 hours Lct. 4W), at the Department of Physics
Assessment: Or. Cr: 10
Lecturer: M. LA CAMERA, Department of Physics

Prerequisites: General Physics I and II, Theoretical Mechanics, Calculus I and II

Syllabus:
Part I Nonlinear Physics
1S (40Lct. 4W) Cr.5

Dynamical systems with a finite number of degrees of freedom. Linear stability analysis of fixed points: bifurcation analysis. Spatially distributed systems, broken symmetries, pattern formation

Part II Chaotic Dynamics
2S (40Lct. 4W) Cr.5

Maps and deterministic chaos. Universal behaviour of quadratic maps. The intermittency route to chaos. Strange attractors in dissipative dynamical systems. The transition from quasiperiodicity to chaos. Regular and irregular motion in conservative systems.

Textbooks:
- G.Nicolis, Introduction to nonlinear science, C.U.P.,
- H.G. Schuster, Deterministic chaos, an introduction, VCH Verlag, Weinheim

Cybernetics and Information Theory
Opt.
Y( 70 Lct. 3W), at the Department of Physics
Assessment: Or. Cr: 10
Lecturer: M. RIANI, Department of Physics.

Prerequisites: General Physics I and II, Calculus I and II

Syllabus:

Part I Dynamical Systems
1S (35 Lct. 3W) Cr: 5

I A- Brief recall to the theory of differential equations. Fundamental theory of dynamical systems. Stability of equilibria. The Poincarè- Bendixon theorem. Periodic attractors.

Textbooks:
- M.H.Hirsch, S,Smale, Differential equations, Dynamical Systems, and Linear Algebra, Academic Press San Diego, 1974: cap. 3,4,5,8,9,10,11,12,13

I B- Non linear dynamical systems: introduction. One- dimensional maps. Universality theory . Fractal dimension. Non linear exemples with chaos. Chos control.

Textbooks:
- S.N. Rasband, Chaotic dynamics of nonlinear systems, J.Wiley and Son, New York, 1989 cap.2,3,4,6

Part II Neural Networks, Stochastic Resonance , Basic Concepts of the Information Theory
2S ( 35 Lct. 3W) Cr: 5

II A- introduction to neural computation. The Hopfield model. Optimization problems. Feed-forward networks: simple perceptrons and multi- layer networks. Unsupervised learning. Applications.

Textbooks:
- J.Hertz, A.Krogh, R.G.Palmer, Introduction to the theory of Neural Computation, Addison-Wesley, Redwood City, 1991 cap.1-9

II B- The phenomenon of stochastic resonance: theory and applications.

Textbooks:
- F.Moss, Stochastic Resonance: from the ice ages to the Monkey's ear. In: G.H.Weiss, Contemporary Problems in Statistical Physics. SIAM, Philadelphia, 1994, p.205-253

II C- Basic concepts of the Information theory: a measure of uncertainty, communication systems, mutual information, elements of encoding.

Textbooks:
- F.M.Reza, An Introduction to Information Theory, McGraw Hill, New York, 1961 cap.1,3,4

Electronics
Opt.
Y(70 hours Lct. 3W), at the Department of Physics.
Assessment: Or. Cr: 10
Lecturer: M. MARINELLI, Department of Physics

Prerequisites: General Physics I and II, Calculus I and II

Syllabus
Part I -Principles of Semiconductor Devices
1S (45 hours, 35 Lct.+ 10 Cla.and Lab.) Cr:5
-Semiconductors Materials. Energy bands and charge carriers in semiconductors. Metals, insulators and semiconductors. Electron and holes. Effective mass. Intrinsic and extrinsic semiconductors. Carrier concentrations.Drift of carriers in electric and magnetic fields. Conductivity and mobility. Excess carriers in semiconductors. carrier lifetime. Quasi-Fermi levels. The charge-neutrality condition. The continuity equation and time-dependent diffusion equations. The Hayness-Shockley experiment.
-Junctions. The contact potential. Equilibrium Fermi levels. Space charge at a junction. Forward- and Reverse- biased junctions, steady state conditions. Transient and A/C conditions. Photodiodes. Solar cells. Fundamentals of bipolar junction transistor operation. Minority carrier distribution and terminal currents. The coupled-diode model. Amplification. Switching. Field-effect transistor. The junction FET. The basic operation of the Metal-Insulator-Semiconductor FET.
-Laboratory experiences: Measurement of the contact potentials by a reed
electrometer. Thermoionic current from a hot filament. Photodiode current.

Part II Semiconductor devices. Lasers. Superconductor devices.
2S (45 hours, 35Lct. + 6 Cla.and Lab. + 4 of stage at the Semiconductor
Divison of Ansaldo)
-Semiconductor devices. Growth of semiconductors. Fabrication of p-n junctions. Reverse-bias brekdown. Recombination and generation in the transition region. Ohmic losses. Metal-semiconductor junctions. Heterojunctions. Tunnel diodes. Light-emitting diodes. Fiberoptic communications. BJT fabrication. High-frequency transistors. Heterojunction bipolar transistor. Integrated circuits. Charge Coupled Devices (CCD). The semiconductor controlled rectifier. Negative conductance microwave devices.
-Lasers. Temporal coherence of a light source. Spatial coherence of a radiation field. Level population inversion. Maser. Light amplification. Three and four levels laser. Semiconductors lasers.
-Superconductive devices. Josephson junction. Josephson relations and the equivalent circuit. Quantum interference in two junction in parallel. DC SQUID. RF SQUID.
Laboratory experiences: Build a flux-locked loop by a lock-in amplifier and an high temperature SQUID. Measure of h/e by the microwave-induced (Shapiro) steps. Stage at the plant for semiconductor power devices of the Ansaldo Semiconductor Division, Genova

Textbooks:
- B.G.Streetman, Solid State Electronic Devices, 4th edition, Prentice Hall
- S. Wang,Fundamentals of Semiconductor Theory and Devices Physics, Prentice Hall.
- L.Solymar, D.Walsh, Lectures on the Electrical Properties of Materials, 5th edition, Oxford Science Publications
- A.S. Grove, Fisica e tecnologia dei dispositivi a semiconduttore, F.Angeli
- Van Duzer, Turner, Principles of Superconductive Devices and Circuits, Elservier
- J.C.Gallop, SQUIDS, The Josephson Effects and Superconducting Electronics, Adman Hilger
- M.Thinkham, Introduction to Superconductivity, 2nd edition, Mc Graw-hill
- O'Shea, Callen, Rhodes, Introduction to Laser and their applications,Addison-Wesley
- Milonni, Eberly, Lasers, J.Wiley

Elementary Particle Physics
Opt.
Y (70 hours Lct. 3W), at the Department of Physics
Assessment: Or. Cr: 10
Lecturer: G. MORPURGO, Autonomous Cathedra.

Prerequisites: Theoretical Physics Institutions, Math. Methods of Physics

Syllabus:
The course is intended to provide a general idea of the main chapters of Particle Physics, dealing with strong electromagnetic and weak interactions. It is theoretically oriented and contains the elements of field theory necessary for developing the subject. The course is divided into two parts:
Part I Introduction, Elements of Field theory, Quantum Electrodynamics
1S(35 hours Lct.3W) Cr:5

Part II Strong interactions, quarks, Spectrum of hadrons, Parton Models,
Weak interactions, Fundamentals and Phenomenology
2S(35 hours Lct.3W) Cr.5

Textbooks:
- G.Morpurgo,"Introduzione alla fisica delle particelle",
Zanichelli,1987.

Elements of Nuclear Physics
Opt.
Y(82 hours) at the Department of Physics
Assessment: Or + Lab. test. Cr: 10
Lecturer: G. RICCO, Department of Physics.

Prerequisities: General Physics I and II.

Syllabus:
Part 1 - General properties of stable nuclei (10 hours).
Part 2 - Interaction of charged and neutral particles with matter (10 hours)
Part 3 - Instability in nuclei (7 hours).
Part 4 - Electromagnetic interaction in nuclei (8 hours).
Part 5 - Strong interaction in nuclei (15 hours).
Part 6 - Weak interaction in nuclei (6 hours).
Part 7 - Leptons (6 hours).
Part 8 - Hadrons and their structure (20 hours).

Textbooks:
- K.N. Mukhin, Experimental Nuclear Physics, vol. I and II; MIR Publishers, Moscow, 1987.
- B. Blanc, Physique Nuclaire, Masson, Paris, 1980.
- E. SegrŠ, Nuclei e particelle, Zanichelli, Bologna.

History of Physics
Opt.
Y( 70 hours Lct.3W ), at the Department of Physics
Assessment: Or. Cr: 10
Lecturer: N. ROBOTTI, Department of Physics

Prerequisites: General Physics I and II, Calculus I and II

Syllabus:
Part I Origins of Quantum Mechanics
(35 hours Lct. 3W) Cr.5
The Physics of "invisible rays" in 19th century. Cathode rays and other phenomena. The discovery of X-Rays, of the electron and of radioactivity. Atomic models in Classical Physics. J.J.Thomson's model. The research program of E.Rutherford. The experiments of scattering of and particles. The atomic nucleus. The origin of Quantum Theory. The problem of the "black-body" and the Hypotesis of quanta of energy. The quanta of radiation. Development of the early quantum conception. The first Solvay congress. Bohr atomic theory. Limits of classical Physics: Nicholson (1911-13) and Rutherford(1913). J.J.Thomson(1910-13). Bohr's theory of the hydrogen atom. The atomic number and the experiments of Moseley.

Part II From the Old Quantum Theory to the New quantum Mechanics
(35 hours Lct.) Cr.5

1 Quantum conditions. Statistical Mechanics and the significance of"h". Sommerfeld's conditions and the theory of hydrogen atom. The fine structure of the line spectra. Zeeman effect and the Stark effect.
2 Principles of old quantum theory. The principle of Adiabatics Invariants. The correspondence principle. Some applications.
3 The transition to Quantum Mechanics. Limits of Bohr- Sommerfeld theory. The Vector Model. The Multiplet structure and the anomalous Zeeman effects. Pauli exclusion principle. The spin of the electron. Open problems and new ideas.
4 The rise of Matrix Mechanics and the formulation of Wave Mechanics

Textbooks:
- M.Jammer, The Conceptual Development of Quantum Mechanics, Mc.Graw-Hill, NY 1966
- J. Mehra, H.Rechenberg, The Historical Development of Quantum Theory 1, vol 1 (part 1 and 2),vol.2, vol.3, Springer- Verlag, NY 1982

Modern Physics
Opt
Y (80 hours Lct. 3W) at the Physics Department.
Assessment: Or Cr: 10
Lecturer: S. VITALE, Department of Physics.
This is a monographic course on modern topics of general physics. In the last years the course was devoted to arguments of nuclear and particles. Astrophysics.

Prerequisites: General Physics, Institution of Theoretical
Physics, Elements of Statistical Mechanics and of Atomic and
Nuclear Physics.

Syllabus:
Part 1- Elements of Observational astronomy: Optical Spectroscopy. Radio, infrared, ultraviolet, X and gamma ray. Astronomy. Background radiation. Stellar evolution and stellar models: Gravitational energy and Thermonuclear processes. Mass- Luminosity relations. Degenerate Stars; Giants and Supergiants.
The Standard Solar model. Thermonuclear reactions of Astrophysical interest. The p-p cycle, 7Be, the CNO cycle, Neutrino Astrophysics : Solar neutrinos, neutrinos from Supernovae.

Part 2- Extra galactic Astrophysics and cosmology: Dynamics of stellar systems and the Virial Theorem. Globular clusters and cluster of Galaxies. Dark Matter. Galaxies expansion. Newtonian and relativistic cosmological models; Measure of cosmological parameters. Universe density. Thermal history of primordial universe. The lepton Era, He abundance and relict neutrinos.

Part 3- Elements of Neutrino Physics : Neutrino interaction and neutrino detectors, neutrino masses, neutrino oscillation. Experiments on the solar neutrino problem and on stellar collapses. Astrophysical and laboratory bounds on neutrino families, masses, oscillations and decay. Experiments on Dark
matter detection.

Textbooks:
- Lecture notes.
Part 1: Longair M.S. High EnergyAstrophysics, Harwit, Astrophysical Concepts.
Part 2: Longair : Lectures on Galaxy Formation.
Part 3: R.N. Mohapatra and P.B.Pal, Massive Neutrinos Physics and Astrophysics.

Molecular Physics
Opt.
Y (80 hours Lct. 3W), at the Department of Physics.
Assessment: Or. Cr:10
Lecturer: M. ROCCA, Department of Physics

Prerequisites: Foundations of Classical physics, Quantum Mechanics and Structure of Matter.

Syllabus:
Part I Molecules and introduction to the physics of surfaces
1S (40 Lct.) Cr 5

Construction of molecular orbitals. Symmetry properties of molecules. Electronic excitations. Roto-vibrational excitations. Selection rules in Rahman and infrared spectroscopy. Frank Condon mechanism and Negative Ion Resonances. Selective bond breaking. Morphology of clean and adsorbate covered solid surfaces. Symmetry aspects and investigation methods. Chemical analysis of the surface. Chemiosorption and physiosorption. Type and role of surface defects.

Part II Advances in Surface Physics
2S (40 Lct.) Cr.5

Electronic surface states. Electronic and vibrational excitations at the surface. Surface reconstruction in metals and semiconductors. Two dimensional phase transitions. Surface diffusion phenomena. Gas-surface interaction. Catalysis. Nanostructures and nano engineering. Surface magnetism.

Textbooks:
- V. Bortolani, R. March, G. Tosi , Interaction of atoms and molecules with solidsurfaces, Plenum Publishing ,1990.
- H. Lueth, Surface Physics, Springer Verlag, 1994.
- W. Bingel Theory of Molecular Spectra, Wiley and Sons Ltd, 1969.

Nuclear Force Theory
Opt.
Y( 70 hours Lct. 3W), at the Department of Physics
Assessment: Or Cr: 10
Lecturer: M. GIANNINI, Department of Physics.

Prerequisites: Institutions of Theoretical physics, Elements of nuclear physics

Syllabus:
Part I The nuclear potentials
1S (35 Lct. 3W) Cr: 5

1.- Invariance principles and conservation laws. Rotations. Generators of infinitesimal transformations and group properties. Group representations. Permutation groups. General properties of the internucleon potential.
2.- Static properties of the deuteron. Quadrupole moment and tensor force. Nucleon-Nucleon scattering at low energies and effective range theory. Phaseshift analysis. Exchange forces and spin-orbit interaction. Repulsive core. Phenomenological potentials
3.- Three-nucleon systems. Brief discussion on Faddeev equations. Nuclear forces and complex nuclei. Single particle configurations. Hartree- Foch equations.
4.- Electromagnetic interactionsin nuclei. Electromagnetic current of fermions. Dirac equation. Nucleon form factors.

Part II Fundamental interactions in nuclei.
5.- Relativistic scattering theory. Dyson equation for the scattering S- matrix. Relation between propagators and and interaction potentials.
6.- Relativistic interaction between fermions and radiation. Electron scattering and form factors. Microscopic interpretation of Coulomb potential.
7.- Physics of pions. Pion-nucleon interactions and meson field. Baryon resonsnces. Meson theory of nuclear forces. Realistic nuclear potentials. Brief discussion on exchange currents.
8.- Internal structure of nucleons. Bag model. Non relativistic Quark model. Elettromagnetic properties of nucleons in the quark model. Nucleon- Nucleon interaction at small distances and role of the colour magnetic interactions.

Textbooks:

- A. G. Sitenko, V. K. Tartakovskij, Lezioni di teoria del nucleo, Mir
- J. M. Eisenberg, W. Greiner, Nuclear theory, North Holland.
- J.D. Bjorken, S.D. Drell, Relativistic Quantum Mechanics, MacGraw-Hill
- M.D. Scadron, Advanced Quantum Theory, Springer

Nuclear Physics
Opt.
Y (60 hours, Lct 3W), at the Department of Physics.
Assessment:Or. Cr: 10
Lecturer: E. BELTRAMETTI, Department of Physics.

Prerequisites: Institutions of Theoretical Physics

Syllabus:

Part I
1S (30 hours, Lct 3W) Cr. 5

(i) Review of nuclear properties;
(ii) Two-body problem at low energies;
(iii) Properties of nuclear forces;
(iv) Nuclear models;

Part II
2S (30 hours, Lct.3W) Cr.5

Many body problems in nuclear physics
Weak interactions in nuclei
Nuclear effects in star evolution

Textbooks:

- Lecture notes

Particle Accelerator Physics
Opt.
Y(60 hours Lct. 3W), at the Department of Physics.
Assessment: Or Cr: 10
Lecturer: M. CONTE, Department of Physics.

Prerequisites: General Physics I and II, Calculus I and II, Theoretical Mechanics.

Syllabus:
1st Module: Introduction to the Physic particle accelerators
1S (40 hours Lct.3W) Cr 5

1) Historical overview on several types of accelerators. The weak focusing principle. Hamiltonian formalism, symplectic transformations and Liouville's theorem. Field expansions of various beam transport magnets. Strong focusing with the concepts of emittance, dispersion and Twiss parameters. Applications demonstrating calculation techniques, optimization of compound optical elements and chromatic effects.
2) Phase stability. Transition energy. Synchrotron oscillations. Synchrotron radiation. Emitted power. Damping of synchrotron and betatron oscillations. Spectrum. Quantum diffusion. Effects on beam characteristics. Linear accelerators. Radio-Frequency Quadrupoles (RFQ).
3) Linear and nonlinear resonances. Coupled motion.
4) Some collective effects. Space charge effects with self-beam and beam-beam interactions. Two methods for circumventing Liouville's theorem: electron and stochastic cooling.

Textbooks:

- M. Conte and W.W. MacKay, An Introduction to the Physics of Particle Accelerators, World Scientific, Singapore, 1991.
- D.A Edwards and M.J. Syphers, An Introduction to the Physics of High Energy Accelerators, John Wiley and Sons, New York, 1993.
- H. Wiedemann, Particle Accelerator Physics, Basic Principles and Linear Beam Dynamics, Springer-Verlag, Berlin, 1993.
- P.J. Bryant and K. Johnsen, The Principles of Circular Accelerators and Storage Rings, University Press, Cambridge, 1993.

Physics Laboratory 2-A
(Nuclear and Subnuclear Physics Laboratory) Cr: 12
Opt.
Y (100 hours, 40 Lct. + 60 Lab.), at the Department of Physics.
Assessment: part I Or.
Assessment: part II Wr reports + Or. presentation
Lecturer: S. SQUARCIA, Department of Physics.

Prerequisites: Institutions of Nuclear Physics.

Syllabus:
Part I

a) Basic nuclear processes in radioactive sources. Alpha decay. Beta decay. Gamma emission. Neutron sources. Range. Cross section. Radiation protection. Passage of radiation through matter. Classical case (Bohr calculation). The Bethe-Bloch formula. Cherenkov effect. Energy loss of heavy charged particles and of electrons. Photon interaction.
b) General characteristics of particles detectors Sensitivity. Detector response. Energy resolution. Dead time. Ionization detectors. Multi-wires proportional chambers. Drift chambers. Time projection chambers. Scintillation detectors. Organic scintillators. Inorganic crystals. Photomultipliers. Basic construction. Photocathode. Dynode. Time response and resolution. Noise.
c) Data acquisition.The NIM standard. Signal transmission. Multichannels analyser. Coincidence techniques.

Part II

a) Data elaboration. Programming in C under UNIX. Network data transmission. Monte Carlo simulation. Minimization methods. Experimental data show.
b) Laboratory experiments
- Planck constant determination via black-body distribution.
- Photoelectric effect and Planck constant determination.
- Electron para-magnetic resonance.
- Rutherford scattering: classical cross-section.
- Compton diffusion and electron mass determination.
- Beta decay and neutrino mass determination.
- Muon: mean life time and Lande` factor determination.

Textbooks:
- A.C.Melissinos, Experiments in Modern Physics - Academic Press (New York) 1966.
- W.R. Leo, Techniques for Nuclear and Particle Physics Experiments -Springer-Verlag (Berlino) 1987.
- G.F.Knoll, Radiation detection and measurement - John Wiley and Sons (New York) 1979.
- F.Sauli: Instrumentation in High Energy Physics - World Scientific (Singapore) 1992
- S. Squarcia, Lectures notes.

Physics Laboratory 2-B
(Low temperature and Surface Physics Laboratory)
Opt.
Y(100 hours, 60 Lct. 3W + 40 Lab. 4W ),at the Department of Physics
Assessment: Or. Cr: 12
Lecturer: G. GALLINARO, Department of Physics.

Prerequisites: General Physics I and II, Calculus I and II

Syllabus:
1) Experimental techniques in low temperatur physics
2) Superconductivity
3) Cryogenic detectors
4) Experimental techniques in surface physics
5) Laboratory experiments
- Carbon thermometer calibration at low temperatures
- Thermoregulation of a superfluid helium bath
- Superconductors magnetic characteristics
- Adiabatic demagnetisation
- Bolometer characteristics at low temperatures
- Giaever junctions characteristics

Textbooks:
- Lecture notes

Physics of Metals
Opt.
Y (70 Lct. 3W), at the Department of Physics
Assesment: Or. Cr: 10

Syllabus:
Part I Normal Metals
1S ( 30 Lct. 3W) Cr: 5
Lecturer: N.BOBEL, Department of Physics.
Prerequisites: Institution of Theoretical Physics

Free electron in a box. Specific heat. The Pauli paramagnetism. Low energy excitations and quasi particles. Electron states and the crystal structure. The Bloc theorem. The Fermi surface. Wave packets. The semiclassical electron dynamics. The Boltzmann equation. Electrical and hermal conductivity. Thermoelectric effects. The Hall effect and the magnetoresistance. Scattering by inpurities and by the crystal vibrations. Electrical conductivity in amorphous systems. Systems of two, one and zero dimensions. Quantum effects.

Textbooks:
- A.A. Abrikosov, Fundamentals of the Theory of Metals

Part II Superconductivity
2S ( 40 Lct. 3W) Cr: 5
Lecturer: A.SIRI, Department of Physics.
Prerequisites: Solid State Physics 1S

The course presents a phenomenologic approach to the Superconductivity:
Superfluid- Ginzburg-Landau theory- Intermediates and mixed states. The properties in the normal and superconducting state of Low Tc and High Tc. Materials are presented.
Superconducting materials: alloys and cuprate oxydes- Properties in normal and mixed state. Applications of superconductivity.
Bulk and film preparation. Josephson effect and squids. Critical current in wires and tapes. Magnets. RF cavities and lines. The microscopic theories are only introduced.
BCS elements and introduction to the Anderson theory of the HTCS.

Textbooks:
- Notes of the lectures
- Tinkham M., Introduction to Suprconductivity, McGraw Hill, 1993

Physics of the Atmosphere
Opt.
Y ( 100, Lct. 3W), at the Department of Physics
Assessment: Or. Cr: 10
Lecturer: R. FESTA, Department of Physics.

Prerequisites: General Physics I and II, Calculus I and II

Syllabus:
Part 1 - Fundamentals of fluid dynamics (30 hours)
Basic concepts and equations; general theorems. Dynamics of incomprehensible non viscous fluid flows: irrotational flows, vortex flows. Dimensional analysis: homogeneity and similarity. Dynamics of viscous fluid flows: exact solutions, boundary layer. Water in fluids. Fluidodynamic stability.

Part 2 - Weather and climate (40 hours)
The structure and constitution of the athmosphere. Solar radiation and global climate. Athmospheric thermodynamics. Athmospheric dynamics. Clouds and precipitation. Smaller-scale weather systems. Large-scale weather systems in mid-latitudes. Large-scale weather systems in low latitudes. Structure and
constitution of the athmospheric boundary layer. The athmospheric engine.

Part 3 - Athmospheric turbulence (30 hours)
The nature of turbulence. Turbulent transport of momentum and
heat. The dynamics of turbulence. Boundary-free shear flows. Wall-
bounded shear flows. Turbulence in the athmospheric boundary
layer. The statistical description of turbulence. Turbulent
transport. Spectral athmospheric dynamics.

Textbooks:
- B.K. Shivamoggi, Theoretical fluid dynamics, Martinus Nijhoff Publishers, Dordrecht (1985)
- J.S. Darrozes and C. Francois, Mecanique des fluides incompressibles, Springer-Verlag, Berlin (1982)
- R. McIlveen, Fundamentals of weather and climate, Chapman &
Hall, London (1992)
G.D. Roth, Guida alla meteorologia, Arnoldo Mondadori Editore,
Verona (1979)
H. Tennekes and J.L. Lumley, A first course in turbulence, The
MIT Press, Cambridge, Massachussets (1972)

Physics of the Condensed States
Opt.
Y( Lct. 3W), at the Department of Physics
Assessment: Or. Cr: 10
Lecturer: G. CASANOVA, Department of Physics.

Radioactivity
Opt.
Y( Lct. 3W), at the Department of Physics
Assessment: Or. Cr: 10
Lecturer:M.SANSONE, Department of Physics.

Relativity
Opt.
Y (90 hours Lct. 3W + Cla. 1W), at the Department of Physics
Assessment: Or Cr: 10
Lecturer: R. COLLINA, Department of Physics.

Prerequisites: General Physics I and II, Calculus I and II, Theoretical Mechanics

Syllabus:
Part 1 - Special Relativity
(35 hours Lct. + 10 hours Cla.) Cr.5

Covariance of the physical laws. Inertial observers. The Lorentz and Poincar‚ groups. Tensors and their algebra. Local formulation and Lagrangian point of view. Electrodynamics and applications.

Part 2 - General Relativity and Gravitation
(35 hours Lct.+ 10 hours Cla.) Cr.5

The Eotvos experiment. The principle of equivalence, Pound-Rebka- Snider experiment. Elements of differential geometry. Einstein's field equation. Deflection of light near the Sun, anomalous perihelion precession end echo-radar experiment. Weak gravity and gravity waves.

Textbooks:
- L. D. Landau, E.M. Lifschitz, Corso di Fisica Teorica, vol. II, Teoria dei Campi, Editori Riuniti Roma.
- S. Weinberg, Gravitation and Cosmology, J. Wiley, New York, 1972.
- J. L. Anderson, Principles of Relativity Physics, Academic Press, New York, London.
- H. Stefan. General Relativity: An Introduction to the Theory of the Gravitational Field, Cambridge University Press, 1982.

Solid State Physics
Opt.
Y(80 hours Lct 3W), at the Department of Physics
Assessment: Or Cr: 10
Lecturers: Andrea Levi and GUGLIELMO BOEBEL, Department of Physics

Prerequisites: Institution of Theoretical Physics, Structure of Matter.

Syllabus:

a) Crystal structure
Point groups. Bravais Lattices. Important Lattices. Reciprocal Lattice. X-Ray scattering. Structure of elements. Ionic Crystal and MADELUNG energy.
b) Electronic states: Drude's model- Hall effect, Plasma oscillations, Wiedemannand Franz's law, Sommerfeld's theory; Bloch theorem, Bloch's states and quasi momentum, Brillouin zones, Bands, Fermi surface, density of states, quas-free electrons, Kronig and Penney's model, effective mass, tight binding, cell of Wigner-Seitz, pseudopotential, semiclassical motion of electrons, Zener tunnelling, closed and open orbits in the hall effect.
c) Transport and optical properties: Metals vs.semiconductors, III-V and II-VI compounds, alloys, optical properties, dielectric function, free electrons don't absorb the light, interband transitions, reflectance, plasmons, Three regimes: Hagen-Rubens relaxation, high frequencies
d) Lattice vibrations: Elasticity theory, Dulong and Petit's law, linear chain, diatomic linear chain, Van Hove's singularities, anharmonicity, Gruneisen's constant, spectrum of an imperfect crystal, instabilities, Lindemann's law, melting theory.
e) Semiconductors: Intrinsic semiconductors, doped semiconductors, high and low temperatures regimes, p-n junction
f) Defects and excitations: vacancies, colour centres, polaritons, excitons, polarons, dislocations, stacking faults, crystal growth
g) Magnetism: Landau states- de Haas- van Halphen effect; necks and bellies of the Fermi surface; Larmor diamagnetism; Paramagnetism: Curie's and Brouillon's law; adiabatic demagnetization; Pauli paramagnetism; origin of ferromagnetism: exchange integral; Heisenberg and Ising Hamiltonians; mean field; Heisenberg chain and Bethe Ansatz; spin waves; critical esponents.
h) Electron gas: Screening, Thomas Fermi atom; Hartree-Fock theory; Density functional. Hohenberg and Kohn's theorem; LDA.

Statistical Mechanics
Opt.
Y ( 50 hours Lct. 3W), at the Department of Physics
Assessment: Or Cr: 10
Lecturer: A. BLASI, Department of Physics.

1) NOTIONS OF THERMODYNAMICS
Thermodynamic potentials - Chemical potential - Gibbs-Duhem relation -Phase rule - Affinity and law of mass action.
2) DYNAMICAL SYSTEMS
Hamiltonian systems - Determinism, predictability and chaos - Phase space - Liouville and Poincar‚ theorems.
3) PRINCIPLES OF STATISTICAL MECHANICS
Foundations - Entropy - Temperature - Canonical description - Free energy - Entropy vs.information
Pressure and work - Open systems -Classical approximation - Perfect gases: Boltzmann, Bose-Einstein, Fermi-Dirac - Imperfect gases - Correlation functions - Liquids.
4) PHASE TRANSITIONS
First-order transitions vs. continuous transitions - Lee-Yang approach -Critical points and critical exponents - Scaling.
5) EXACTLY SOLVABLE MODELS
Site models and bond models -The Ising chain - The antiferromagnetic Heisenberg chain - The Bethe Ansatz -An introduction to the two-dimensional Ising model.
6) THE 6-VERTEX MODEL
Models for ice and ferroelectrics - The 6-vertex model -The F and KDP cases - Line conservation - The transfer matrix -Thermodynamic limit - The ferroelectric phases - The disordered phase - The
antiferroelectric phase - An infty order transition -What about 5 and 8 vertex models? - Application to surfaces.
7) STOCHASTIC PROCESSES
Definitions - The Markov property - The Wiener-Hin\v{c} in theorem- Master equation - Fokker-Planck equation.
8) NON-EQUILIBRIUM AND IRREVERSIBILITY
Derivation of the master equation - Solution of the master equation -Macroscopic consequences of the master equation -Time and space-time correlation functions -Fluctuation-dissipation theorem - Kubo formulae.

Theoretical Physics
Opt.
Y (110 hours, 70 Lct. 3W and 40 Cla. 2W), at the Department of
Physics
Assessment: Wr. (4h) + Or.(1h). Cr: 12
Lecturer: C. M. BECCHI, Department of Physics.

Prerequisites: Institutions of theoretical Physics, Math. Methods
of Physics

Syllabus:
I Part. Quantum Mechanics of Many Body Systems.
1S(55 hours, 35 Lct. 3W and 20 Cla. 2W)

The Second Quantization Algorithm for fermions and bosons. The linear canonical transformations in the Fock space. The degenerate states of free particles. Quantization of the elastic field. Electron-phonon interaction. An elementary approach to superfluidity and superconductivity based on the canonical transformations.

II Part. Relativistic Quantum Field Theory.
2S(55 hours, 35 Lct. 3W and 20 Cla. 2W)

The Relativistic Classical Field Theory. Locality and Covariance. Noether Theorem. The quantization of the charged scalar field. Spinors. The relativistic theory of electrons and neutrinos. The discrete symmetries P, C and T. The Relativistic Theory of Scattering. The Reduction Formulae. The Green functions and their Functional Generator. The Feynman functional integral formula. The Covariant Perturbation Theory and the loop expansion. The Feynman rules for QED and for the scalar model. Study of cross sections and life times.

Textbooks:
- C. M. Becchi, Lecture notes.

Biological Physics
Opt.
Y (60 Lct. 3W) at the Department of Physics
Assessment Or Cr.10
Lecturer: A.GLIOZZI, Department of Physics

Prerequisites: General Physics I and II, Calculus I and II

Syllabus:
Part I Intermolecular forces
1S (30 Lct. 3W) Cr.5

Strong intermolecular forces; Covalent and Coulomb interactions; interactions involving polar molecules; interactions involving polarization of molecules; Van der Waals forces; Hydrofobic and Hydrophilic interactions; thermodynamicaspects of interfacial equilibria; fluid like structures and self-assembly systems; Nerst and Gibbs; Donnan equations; electrified interfaces; Poisson-Boltzmann and Gouy-Chapman equations

Part II Transport Processes
2S (30 Lct. 3W) Cr.5

Diffusion equations; Brownian motion; Smolouchowsky equation; electrodiffusion; Nerst-Plank equation; Eyring theory; coupling between flows; coupling between chemical reactions and diffusion processes. Excitable membranes. The action potential; molecular basis of exitation; ionic channels; Hodgkin-Huxley theory

Textbooks:
Israelchivilli J., Intermolecular and Surface Forces, Academic Press
Gibish and Tosteson, Membrane Tranport in Biology, Ussing et al.
Cantor and Schimmel, Biophisical Chemistry, W.H.Freeman Editor
Hille T., Ionic Channels of Excitable Membranes

Laboratory of Biological Physics

Cmp.
Y (90 , 18 Lct.+ 72 Lab.) at the Department of Physics
Assessment Or +Lab. Cr.12
Lecturer: M.ROBELLO, Department of Physics

Syllabus:
Part I Models of biological systems
1S (45 hours, 9 Lct.+ 36 Lab.) Cr.6

Experimental models of biological membranes: liposomes- Study of the fusion processes using fluorescence techniques.
Patch-clamp technique in cultured neurons. Measurements of voltage and ligands activated ionic currents
Simulation of protein dynamics and computer graphic.

Part II Advanced microscopy
2S (45 hours, 9 Lct.+ 36 Lab

Fluorescence microscopy in monolayers at air-water interface
Confocal laser scanning microscopy of the morphology and calcium signalling of neurons. Imaging techniques.
STM and AFM microscopy utilised for imaging organic systems at molecular resolution.

Physical Application of group theory

Opt.
Y (60 Lct. 3W ) at the Department of Physics
Assessment Or ( 1h) Cr.10
Lecturer: G.CASSINELLI, Department of Physics

Prerequisites:
Part I: Linear algebra and elementary quantum mechanics
Part II: Linear algebra and some basic results in functional analysis. Quantum mechanics.

Syllabus:
Part I Basic properties of finite dimensional representations of finite groups
1S (30 Lct. 3W) Cr: 5

Examples. Elementary properties of rotation groups, their representations and applications in quantum mechanics. Representations of the symmetric group and their relation with the symmetry classes of tensors. Finite dimensional representation of SU (n).

Part II
2S ( 30 Lct. 3W) Cr: 5

Vector bundles. Associated vector bundles and induced representations. Induced representations of semidirect products. Applications: unitary irreducible representations of the Poincaré group. Dirac theory and Gupta-Bleuler theory.

Textbooks:
- G.Cassinelli, Lecture notes.

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