REAL NUMBERS AND OTHER INTRODUCTORY SUBJECTS
The rationals; $\sqrt 2$ is irrational. The real numbers contain the rationals and have the sup property. A distance on the reals; functions and sequences; limits of sequences. Monotone sequences always admit a limit; series with positive terms; the comparison test, the condensation test, the root and ratio test. Cauchy sequences; series with non-positive terms; absolute convergence and convergence. The Leibnitz convergence theorem. power series and convergence radius. Definition of sine, cosine, exponential and logarithm through their series; important limits.

REAL FUNCTIONS
Definition of the limit of a function; continuous functions; power series are continuous; uniform continuity; a continuous function in a closed and bounded interval is uniformly continuous. The intermediate value theorem; the theorem of Weierstrass. The derivative; differentiability implies continuity; the derivative in the point of maximum is zero. The chain rule and the derivative of the inverse. The theorems of Rolle and Lagrange. Convex functions; the slope of their chords is increasing; if they are differentiable, the derivative is increasing. Inequalities among the means and Young's inequality. Two versions of L'Hopital's theorem. Taylor's formula with the remainder in the forms of Lagrange and of Peano. Convergence of Taylor series: counterexamples and examples. The relationship between convergence of sequences and of functions.

INTEGRATION
Riemann's integral; integration by parts and by substitution; fundamental theory of calculus. The complex numbers; the complex plane and Euler's representation. Integration of rational functions. Taylor's formula with integral remainder. Improper integrals; absolute integrability. Uniform convergence for sequences and series of functions. Limits of Riemann integral under uniform convergence. Power series can be integrated and differentiated term by term.

NERDY THINGS
Various approximations of $\sqr 2$; machin's formula for $\pi$; the infinite product of Wallis; the formula of De Moivre Stirling; the area under the Gaussian with the formula of Wallis; Euler's summation formula; a model of the distribution of wealth; a continuous but nowhere differentiable function.

B. Palumbo - M.C. Signorino, Funzioni algebriche e trascendenti, ed. Accademica, 2015.

Marcellini-Sbordone, Analisi Matematica 1.

De Marco-Mariconda, Analisi Matematica 1.

File system in Linux enviroment. First principles of the C++ programming language.

Stanley B. Lippman, Josée Lajoie, Barbara E. Moo
C++ Primer, Fifth Edition
Addison-Wesley 2012

Any C++ programming language manual

- Linear algebra: linear equations, matrices, Gauss-Jordan reduction, rank of a matrix, solutions of systems of linear equations, sum and product of matrices, invertible matrices and their construction, Rouchè-Capelli theorem.
- Square matrices and determinants: definition of determinant, properties of determinants, determinants and invertible matrices.
- Vector spaces: the example of geometric vectors, definition and examples of vector spaces, linearly independent vectors, independence, finitely generated vector space, basis, change of basis
- Scalar products: definition, euclidean spaces, examples of scalar products, perpendicularity, orthogonal basis, orthonormal basis and orthogonal matrices.
- Cartesian cordinates: coordinates on an affine euclidean space, fundamental metric properties, basic affine and euclidean geometry in dimension n.
- Plane and Space Geometry: isometries of the euclidean plane - points, straight lines, circles in the plane, angle between two straight lines, metric formulae for plane geometry, straight lines and planes in a space, equations of straight lines, planes, spheres, circles.
- Linear maps: Kernel and Image of a linear map, associated matrix after fixing the basis, linear operators, eigenvalues and eigenvectors of a linear operator, characteristic polynomial, search for eigenvalues and eigenvectors
- Quadratic equations: conics in the cartesian plane, conics and symmetric matrices, classification up to isometries, canonical form of a conic, metrical properties, quadrics in the space, type and canonical form.

Suggested texts: F. Flamini, A. Verra Matrici e Vettori. Carocci Editore.

Experimentation in Physics 1
Physical quantities. Intensive and Extensive physical quantities. Direct and indirect measurements. Base and Derivatives quantities .
Unit of measure. Systems of measurements units. The International System and the cgs systems. Changing units of measure.
Physical dimensions and dimensional analysis.

Measurement Instruments. Analog and Digital Instruments. Counters. Measurement instruments features:
Linearity, Sensitivity and Accuracy. Uncertainty in measurements. Errors and uncertainties. Causes of uncertainty.
Type A and Type B uncertainties. Random errors and systematic effect.

Presentation and graphic analysis of data. Charts for Data Representation and Analysis. Linear, semi-logarithmic, double-logarithmic graphs.
Methods of linearization of mathematical relations. Histograms.

Probability. Definitions of probability: Classical, Frequentist and subjective. Probability of the Sum of Events. Probability of the Product of Events.
Conditional Probability. Bayes Theorem. Probability distributions. Discrete and continuous distributions. Cumulative probability distribution.
Binomial and Poisson distribution. Continuous distributions. Probability density distribution. Definition of expected value.
Moments of distributions. Central moments of distributions. Mean value and Variance. Skewness and Kurtosis.
Average value and variance of Binomial, Poisson, Uniform, Gaussian, Exponential, t-Student and Cauchy distributions. Multivariate Distributions.

Statistical tools.
Tchebicheff's Inequality. The Law of the Great Numbers. The central limit theorem. Sample average and sample variance.
Estimation of the mean sample value and formula for estimating sampling variance.

Uncertainty in indirect measurements. Propagation of uncertainties. Independent variables.
Propagation of uncertainties in the case of monomous formulas. Related random variables. Definition of correlation coefficient.
Composition of type A and type B uncertainties.

Estimation of parameters. Least square method. Maximum Likelihood method. High likelihood stimuli.
Examples of applications of Least square and Maximum Likelihood methods.
The concept of confidence interval and level.


Chi square test. Chi square test for functional relations. Pearson square square test for histograms.

Experiments: Measurements of Lengths. Measurement of Density. Verification of Boyle-Mariotte law.
direct method. Experiment for the determination of the spring constant.
The pendulum. Measurement of gravitational acceleration with a reversible pendulum.

C. Bini - Lezioni di Statistica per la Fisica Sperimentale - Edizioni Nuova Cultura. Roma 2011

Vectors and vector calculus: definition of a vector, its representation in cartesian and polar coordinates, carrier, properties, dot product, vector product, mixed product.

Material point kinematics: position, velocity, scalar and vector acceleration of a material point. Centripetal and tangential acceleration. Uniformly accelerated motion, uniform and not uniform circular motion, harmonic motion. speed and acceleration in polar coordinates. Areolar speed.
Law of composition of speeds and accelerations; relative motion.

Mechanics of point systems: the Galileo’s first principle of dynamics and Galileo’s relativity. Inertial reference frame. Second and third law of dynamics. Elastic forces, static and dynamic friction, viscosity; applications.
Transformation of coordinates and laws of composition of speeds and accelerations in general; acceleration of Coriolis.
Inertial reference frame and apparent forces: the centrifugal force and the Coriolis force.
Impulse of a force, quantity of motion and their relationship. The moment of force, the angular momentum and their relationship; central forces and pendulum.
The work of a force, kinetic energy and the theorem of kynetic energy. Conservative forces and potential energy, the law of conservation of mechanical energy.
Universal law of gravitation, potential energy and applications. Inertial mass and gravitational mass. Kepler's laws and their explanation using Newton laws.

Material point systems: the cardinal equations of mechanics. Center of mass, definition, properties and the theorem of the center of mass.
The conservation of the quantity of motion and of the angular momentum in isolated systems. Energy of a point system, the Koenig theorem. Two-point systems: reduced mass.
Collisions between material points: elastic and anelastic collisions.

Mechanics of rigid body: translation and rotation, characteristics and vector representation; decomposition of motion in translation and rotation; arbitrariness of the translation and uniqueness of the rotation. Quantity of motion, angular momentum and kinetic energy of a rigid body. Moment of inertia, Steiner's theorem.
Relationship between angular moment and angular velocity of a rigid body, main axes of inertia. Analysis of the motion in systems with a fixed axis rotation, with a rotation axis moving parallel to itself, with a fixed point; gyroscope, trowel and gyroscopic compass.

Mechanics of fluids: pressure, definition and properties. Fluids at rest: law of Stevin, of Pascal, of Archimedes.
Fluids in motion: mass storage in stationary flow, Bernoulli equation.
Laminar motion, viscosity and the law of flow rate.
Touch upon the turbulent motion and the Reynolds number. The motion of a body in a fluid.

Thermodynamics: temperature and its microscopic meaning, heat, definitons and heat transmission: conduction, convection, irradiation.
Transformations of a thermodynamic system, reversible and irreversible transformations: the work in a transformation.
First law of thermodynamics, internal energy.
Perfect gases and their transformations, real gases, solids and liquids. Transformation between phase states of matter.
Second law of thermodynamics: classic statements, thermal engines; the Carnot engine, the Carnot’s theorem and its generalization; entropy, definition, properties and calculation in transformations of a gas or of simple systems.
Kinetic theory of gases: internal energy and entropy of the perfect gas. Third law of thermodynamics. Thermodynamic potentials: Helmotz free energy and Gibbs free enthalpy, applications. Equation of Clausius-Clapeyron

Elasticity: Hooke's law, Young's module and Poisson coefficient. Volume elasticity, shape elasticity; relationship between elastic constants. Plastic deformations.

Waves: mathematical representation of waves. Transverse waves: waves in the strings; longitudinal waves: compression waves, the sound. Energy of the waves. Doppler effect.

Relativity: Galileo’s relativity and Einstein's relativity: the axioms of special relativity and their consequences, time dilation, length contraction; Lorentz's transformations and speed composition. Mass, energy, impulse and equation of motion in special relativity.

The recommended textbook is:
C. Mencuccini e V. Silvestrini:
Fisica: Meccanica e Termodinamica
Casa Editrice Ambrosiana

In addition, for a better understanding of how to apply Physics to specific situations, student should use also one of the two following textbooks:

D. Halliday, R. Resnick, J. Walker:
Fisica I
Casa Editrice Ambrosiana

or

R.A. Serway, J.W. Jewett Jr:
Fisica per Scienze ed Ingegneria vol. 1 - Quarta Edizione
Casa Editrice EdISES

Atomic Structure
Chemical bonds and Molecular structure
Chemical compounds and reactions
Aggregation states
Thermodynamics
Solutions
Kinetics
Chemical equilibrium
Reactions in solution
Electrochemistry

M. Schiavello, L. Palmisano; “Fondamenti di Chimica”, Edises
P. Michelin Lausarot, G. A. Vaglio; “Stechiometria per la Chimica Generale” Piccin

Electric charge. Coulomb's law. Quantization of the electric charge.
The electric field. The elctrostatic potential. Electric dipole.

Gauss's theorem. Electrostatic shielding. Capacitance. Capacitors.
Series and parallel connection of capacitors. The general problem
of electrostatics. Energy of the electrostatic field.

The dielectric constant. Polarization by deformation and orientation.
The electric polarization vector. The equations of elettrostatics with
dielectrics. The D vector.

Electromotive force. Electric current and current density. Ohm's law.
Joule's law. Resistance. Resistors. Series and parallel connection of resistors.
Kirchhoff's laws. Electric generators. Currents in liquids and gases.

Magnetic field. Lorentz force. Magnetic field from a moving charged particle.
Laplace's laws. Divergence of B. Electrodynamical forces. Magnetic moment.
Ampere's law. Faraday's law of induction. Self and mutual induction.
Displacement current.

Magnetic moment of an electron. Magnetic polarization. Current densities.
The equation of magnetostatics in the presence of materials. The H vector.
Dia-, para- and ferromagnetic materials. Larmor's precession. Polarization
by orientation.

Electromagnetic waves. Equation of waves. Plane waves.
Waves in dielectrics. Poynting's vector. Doppler effect. Reflection and
refraction. Dispersion of light. Huygens-Frenel's principle. Interference.
Diffraction. Geometric optics: mirrors and lenses.

Postulates. Time dilation and length contraction. Lorentz transormation.
Four-vectors. Lorentz invariant quantities. Space-time intervals. Velocity.
Four-momentum. Mass and energy. Minkowski's force. Doppler effect.
Four-current. Electromagnetic tensor.

Corrado Mencuccini, Vittorio Silvestrini.
Fisica 2. Elettromagnetismo-ottica. Corso di fisica per le facoltà scientifiche. Con esempi ed esercizi
Liguori Editore

Conservative mechanical systems. Qualitative analysis of motion and Lyapunov stability. Planar systems and one-dimensional mechanical systems. Central motions and the two-body problem. Change of frames of reference. Fictitious forces. Constraints. Rigid bodies. Lagrangian mechanics. Variational principles. Cyclic variables, constants of motion and symmetries.
Hamiltonian mechanics. Liouville's theorem and Poincaré's recurrence theorem. Canonical transformations. Generating functions. Hamilton-Jacobi method and action-angle variables.

G. Gentile, Introduzione ai sistemi dinamici. 1. Equazioni differenziali ordinarie, analisi qualitativa e alcune applicazioni, available online
G. Gentile, Introduzione ai sistemi dinamici. 2. Meccanica lagrangiana e hamiltoniana, available online

ELECrTICAL CIRCUITS
Ideal components: Resistor, Capacitor, Inductor. Active components: current generator, voltage generator. Real components: Resistor, Capacitor, Inductor, Generator.
DC Circuits
Kirchhoff’s Laws, the method of nodes, the method of meshes. The Wheatstone's Bridge. Linear networks: Superposition theorem, Thevenin’s theorem, Norton's theorem, Reciprocity theorem.

MEASUREMENTS in DC Circuits
Current and Voltage Difference measurements, digital voltmeter, ohmmeter. Resistance measurements: voltmeter-ammeter method. Uncertainty in electrical measurements

Alternating Current Circuits
Periodic, alternating, sinusoidal signals. AC coupling. Components in AC circuits, solution of AC circuits: the symbolic method.

AC basic Circuits
RC circuits: low-pass, high-pass, RL circuits. Differentiator and integrator circuits. Resonant circuits: the RLC circuit, series and parallel. The compensated voltage divider.

The digital oscilloscope
Amplitude measurements, phase measurements. Measurement uncertainty.

Pulsed Circuits
Impulsive signals: step signal, pulse signal, rectangular waveform. RC circuits: high-pass, low-pass. Compensated voltage divider.

The transmission line
Model of the transmission line, telegrapher equation, lossless line. Reflection and transmission coefficients. The coaxial cable.

Basic statistical methods
Mean, standard deviation, propagation of errors, confidence limits of a measurement.
Chi-squared test. Graphs, fitting procedures. The gnuplot package

Elementary optics
Basic geometrical options. Optical interference. Optical diffraction.

Class Notes
R. Bartiromo, M. De Vincenzi - "Electrical Measurements in the laboratory Practice" - Springer
M. Severi - "Introduzione alla Esperimentazione Fisica" - Zanichelli
C.K. Alexander, M.N.O. Sadiku - "Circuiti Elettrici" - McGraw Hill
Young - "Elaborazione statistica dei dati sperimentali"
Taylor - "Introduzione all'analisi degli errori"
Any textbook on Physics, Electronics e Statistics for the degree course on Physic

The learning process designed for this subject is based on the following activities:
lectures by the teaching faculty and laboratory exercises.
More details will be available to students at the beginning of the course on the website: http://host.uniroma3.it/laboratori/escher/ProfSchirripa.htm.

Course Syllabus
Fundamental concepts in electronics applied to measurements. Introduction of theory of solid state electronics including semiconductor physics, diodes, BJT, MOSs. Fundamental of amplifiers and principles of feedback. Applications of operational amplifiers. Fundamental topics on digital electronics and application of logical gate.
The lectures are complemented by laboratory exercises (with compulsory attendance).
The purpose of the laboratory exercises is to give students hands-on experience to allow them to test electronic components who have studied during lectures. Students will be required to carry out the laboratory exercises and collect their data and present a written report. The report must be submitted within the following week for evaluation.
List of laboratory exercises
Direct measurement of the speed of light
Applications of circuits with diodes
Determination of Planck’s constant using Light Emitting Diodes (LEDs)
Exercises with operational amplifiers
Exercises with BJT and MOS
Applications of Logical gates

Exam Modalities
The exam consists of an oral exam on the theoretical aspects discussed in class and a critical analysis of the various laboratory exercises.

Materials Provided by Professor website:
http://host.uniroma3.it/laboratori/escher/ProfSchirripa.htm

QUANTUM MECHANICS: THE CRISIS OF CLASSICAL PHYSICS. WAVES AND PARTICLES. STATE VECTORS AND OPERATORS. MEASUREMENTS AND OBSERVABLES. THE POSITION OPERATOR. TRANSLATIONS AND MOMENTUM. TIME EVOLUTION AND THE SCHRODINGER EQUATION. PARITY. ONE-DIMENSIONAL PROBLEMS. HARMONIC OSCILLATOR. SYMMETRIES AND CONSERVATION LAWS. TIME INDEPENDENT PERTURBATION THEORY. TIME DEPENDENT PERTURBATION THEORY. ROTATIONS AND ANGULAR MOMENTUM. ORBITAL ANGULAR MOMENTUM. SPIN. ANGULAR MOMENTUM COMPOSITION. IDENTICAL PARTICLES. THE HYDROGEN ATOM.

Lecture notes available on the course website

J.J. Sakurai, Jim Napolitano - Meccanica Quantistica Moderna - Seconda Edizione [Zanichelli, Bologna, 2014]
An english version of the book is also available:
Sakurai J.J., Modern Quantum Mechanics (Revised Edition) [Addison-Wesley, 1994]

Quantum mechanics: The crisis of classical physics. Waves and particles. State vectors and operators. Measurements and observables. The position operator. Translations and momentum. Time evolution and the schrodinger equation. Parity. One-dimensional problems. Harmonic oscillator. Symmetries and conservation laws. Time independent perturbation theory. Time dependent perturbation theory. Rotations and angular momentum. Orbital angular momentum. Spin. Angular momentum composition. Identical particles. The hydrogen atom.

Lecture notes available on the course website

J.J. Sakurai, Jim Napolitano - Meccanica Quantistica Moderna - Seconda Edizione [Zanichelli, Bologna, 2014]
An english version of the book is also available:
Sakurai J.J., Modern Quantum Mechanics (Revised Edition) [Addison-Wesley, 1994]

- Complex numbers
- Analytic functions
- Integration of complex functions
- Power series
- Integration using the Residue theorem
- Asymptotic expansions
- Vector spaces
- Euclidean spaces
- Eigenvalue problems in N and infinite-dimensional vector spaces
- Function of a matrix
- Distributions
- Fourier transform
- Integral operators and integral equations
- Sturm-Liouville operators
- First order partial differential equations

C. Bernardini, O. Ragnisco and P.M. Santini
Metodi matematici della Fisica, NIS 1993

B. Chabat, M. Lavrentiev
Methodes de la Theorie des fonctions d'une variable complexe, MIR 1972

A. I. Markusevic
Elementi di teoria delle funzioni analitiche, Editori Riuniti 1988

P. Dennery, A. Krzwicki
Mathematics for Physicists, Harper and Row, 1967

The proton, cathode rays, the electron, mass and electric charge.
Black body radiation, Planck
constant, photoelectric effect, X rays, Compton effect, the
photon. Bohr atomic model, atomic
spectra, electron magnetic moment and spin.
Special relativity, Lorentz transforms, four
-
vectors and relativistic invariants, energy and
momentum, relativistic kinematics.
Cross section, absorption coefficient. Coulomb sca
ttering, Rutherford cross section. Scattering of
electromagnetic radiation by a charge, Thomson cross section.
Quantum mechanics and perturbation theory, transition probability, phase space. Decay low,
electromagnetic interaction, emission and absorption,
electric and magnetic dipole radiation,
selection rules. Rutherford scattering, electric form factor, scattering of a charge by a magnetic
moment, electric and magnetic form factor of proton and neutron. Potential scattering, partial
waves, scattering and
absorption cross section.
Properties of nuclei, atomic and mass number, stability band, measurement of charge, mass and
nuclear radius. Statistics, spin and parity of nuclei, the neutron. Electromagnetic energy of nuclei,
magnetic dipole and electric quadr
upole moments.
Fermi gas model, kinetic energy of nucleons. Liquid drop model,
Bethe
-
Weizsaeker
mass
formula, mirror nuclei. Magic numbers, shell model, spin
-
orbit interaction, energy levels and
spin
-
parity states. The neutron
-
proton system, the deuteron.
Nuclear decays, activity. Phenomenology of gamma decay, multipole radiation,
Weisskopf
coefficients. Phenomenology of alpha decay, kinematics, stability curve, potential barrier and
Gamow factor, lifetime. Phenomenology of beta decay, the neutrino hypothe
sis, Fermi theory,
Kurie plot, lifetime, Fermi and Gamow
-
Teller transitions. Weak interaction and Fermi constant.
Discovery of the neutrino.
Nuclear reactions, Fission, energy balance of the Uranium fission, neutron
-
induced fission,
nuclear reactor.
Fusion, cycles of the Sun, energy balance, nucleo
-
synthesis, fusion in the
laboratory.
Nuclear forces, Yukawa model. Cosmic rays, primary and secondary components, the positron.
Discovery and properties of elementary particles, meson and baryons, anti
-
part
icles. Elementary
particle interactions: nuclear, electromagnetic, weak. The quark model, discovery of quarks.

W. E. Burcham and M. Jobes, Nuclear and Particle Physics, Pearson Education
.
• A.Das and T.Ferbel, Introduction to Nuclear and Particle Physics, 2nd Edition, World
Scientific, 2003.
• B.Povh, K.Rith, G.Sholtz,
F.Zetsche: Particelle e nuclei, Bollati Boringhieri, 1998.
• Appunti del corso di Istituzioni di Fisica Nucleare e Subnucleare,
http://www.fis.uniroma3.it/~ceradini/efns.html

The proton, cathode rays, the electron, mass and electric charge.
Black body radiation, Planck
constant, photoelectric effect, X rays, Compton effect, the
photon. Bohr atomic model, atomic
spectra, electron magnetic moment and spin.
Special relativity, Lorentz transforms, four
-
vectors and relativistic invariants, energy and
momentum, relativistic kinematics.
Cross section, absorption coefficient. Coulomb sca
ttering, Rutherford cross section. Scattering of
electromagnetic radiation by a charge, Thomson cross section.
Quantum mechanics and perturbation theory, transition probability, phase space. Decay low,
electromagnetic interaction, emission and absorption,
electric and magnetic dipole radiation,
selection rules. Rutherford scattering, electric form factor, scattering of a charge by a magnetic
moment, electric and magnetic form factor of proton and neutron. Potential scattering, partial
waves, scattering and
absorption cross section.
Properties of nuclei, atomic and mass number, stability band, measurement of charge, mass and
nuclear radius. Statistics, spin and parity of nuclei, the neutron. Electromagnetic energy of nuclei,
magnetic dipole and electric quadr
upole moments.
Fermi gas model, kinetic energy of nucleons. Liquid drop model,
Bethe
-
Weizsaeker
mass
formula, mirror nuclei. Magic numbers, shell model, spin
-
orbit interaction, energy levels and
spin
-
parity states. The neutron
-
proton system, the deuteron.
Nuclear decays, activity. Phenomenology of gamma decay, multipole radiation,
Weisskopf
coefficients. Phenomenology of alpha decay, kinematics, stability curve, potential barrier and
Gamow factor, lifetime. Phenomenology of beta decay, the neutrino hypothe
sis, Fermi theory,
Kurie plot, lifetime, Fermi and Gamow
-
Teller transitions. Weak interaction and Fermi constant.
Discovery of the neutrino.
Nuclear reactions, Fission, energy balance of the Uranium fission, neutron
-
induced fission,
nuclear reactor.
Fusion, cycles of the Sun, energy balance, nucleo synthesis, fusion in the
laboratory.
Nuclear forces, Yukawa model. Cosmic rays, primary and secondary components, the positron.
Discovery and properties of elementary particles, meson and baryons, antiparticles. Elementary
particle interactions: nuclear, electromagnetic, weak. The quark model, discovery of quarks.

W. E. Burcham and M. Jobes, Nuclear and Particle Physics, Pearson Education
.
• A.Das and T.Ferbel, Introduction to Nuclear and Particle Physics, 2nd Edition, World
Scientific, 2003.
• B.Povh, K.Rith, G.Sholtz,
F.Zetsche: Particelle e nuclei, Bollati Boringhieri, 1998.
• Appunti del corso di Istituzioni di Fisica Nucleare e Subnucleare,
http://www.fis.uniroma3.it/~ceradini/efns.html

CONTENTS OF THE LECTURES: the numbers in round brackets refer to the chapter and section of the textbook adopted.
Kinetic theory of gases. Boltzmann equation and H theorem. (1, Par.2.1,2.2,2.3,2.4)
Maxwell-Boltzmann distribution. (1, Par. 2.5)
Phase space and Liouville theorem. (1, Par. 3.1,3.2)
Gibbs ensembles. Micro canonical ensemble. Definition of entropy. (1, Par. 3.3,3.4)
The ideal gas in the micro canonical ensemble. (1, Par. 3.6)
The equipartition theorem. (1, Par. 3.5)
The canonical ensemble. (1, Par.4.1).
The partition function and the free energy. Fluctuations of energy in the canonical ensemble. (1 Par. 4.4)
The grand canonical ensemble. The grand potential. The ideal gas in the grand canonical ensemble. (1 Par. 4.3).
Fluctuations of the particle number. (1 Par. 4.4)
Classical theory of the linear response and fluctuation-dissipation theorem. (1, Par. 8.4).
Einstein and Langevin theories of the Brownian motion. (Par. 1 par. 11.1,11.2).
Johnson-Nyqvist theory of thermal noise. (1 Par. 11.3).
Quantum statistical mechanics and the density matrix. (1, Par. 6.2,6.3,6.4)
Fermi-Dirac and Bose-einstein quantum statistics. ( 1, Par. 7.1)
The Fermi gas. The Sommerfeld expansion and the electron specific heat. (1, Par. 7.2)
The Bose gas. The Bose-Einstein condensation. (1, Par. 7.3)
Quantum theory of black-body radiation. (1, Par. 7.5)


Web page with additional material about the lecture course

https://sites.google.com/a/personale.uniroma3.it/robertoraimondi/home/teaching/elementi

C. Di Castro and R. Raimondi, Statistical Mechanics and Applications in Condensed Matter, Cambridge University Press, 2015.

1- Bohr model for hydrogen-like atoms. Absorption and emission spectroscopic series. Quantum theory for the hydrogen-like atoms. The Schroedinger equation of an electron in Coulomb field. Eigenfunctions and energy levels. Classification of states. Some properties of the radial atomic functions.

2- Interaction of hydrogen-like atoms with the e.m. field. Time dependent perturbation theory for the interaction of electron with the e.m. field. Absorption and emission terms. Transition probability for the absorption and stimulated emission. Cross section for the absorption. Spontaneous emission. Dipole approximation. Selection rules.

3- Grotrian diagram. Polarization of radiation and helicity of the photons. Einstein coefficients.
Form of the lines due to the lifetime of the levels.

4- Relativistic corrections. Spin-orbit interaction. Darwin correction. Fine structure corrections for the hydrogenic atoms.

5- Effects of electric and magnetic static fields. Stark effect. Normal Zeeman effect. Paschen-Back effect. Anomalous Zeeman effect.

6- Definition of atomic units. Atoms with two electrons. Approximation of independent electrons. Interaction
electron-electron as a perturbation. Variational method. Excited states. Coulomb energy and exchange energy
for states with two electrons. Energy levels in the continuum .

7- Many-electron atoms. Approximation of central field. Diagram of levels. Many-particle wave function, Slater determinant. Hartree-Fock equations and exchange term.

8- Diagram of levels and Hund's rules. LS coupling. Hund's rule in the presence of the spin-orbit term. Examples of energy levels for
not equivalent and equivalent electrons. J-j coupling.

9- Selection rules for atoms with many electrons in the dipole approximation.
Spectra of alkali atoms, the quantum defect. Atomic spectra of He and alkaline earths.

10- Molecular Physics. Born-Oppenheimer approximation. Schroedinger problem
for electrons. Equation for the nuclei.

11- The hydrogen molecular ion. Applications of the LCAO method. Symmetry properties of
diatomic molecules. Hydrogen molecule with the molecular orbital method. LCAO method in general.
Bonding and antibonding states. Covalent and ionic bonding.

12. Dynamics of nuclei. Rotational and vibrational levels. Total angular momentum of the nuclei and the electrons.

13- Morse potential. Anharmonic corrections. centrifugal corrections to the Morse potential.

14. Transitions between vibrational and rotational levels. Selection rules. Examples of eteronuclear and diatomic molecules.
Raman effect. Electronic transitions.

15- Franck-Condon principle.

B. H. Bransden and C. J. Joachain "Physics of Atoms and Molecules" (I-st or II-nd edition)