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CODE 57227
SEMESTER 2° Semester
Propedeuticità in ingresso
Per sostenere l'esame di questo insegnamento è necessario aver sostenuto i seguenti esami:


The course aims to provide a general picture of modern physics. Starting from  statistical thermodynamics and from the theories of mechanical and electromagnetic waves we will proceed to the discussion of the transition from classical to quantum physics with some hints to the theory of relativity. Particular emphasis will be placed on the common features of classical wave theory and wave mechanics, on the discussion of experiments and on the solution of simple problems.



The course aims to provide a good level of knowledge of the main quantum effects in atoms, nuclei and molecules, gases and condensed matter


The aim of the course is to bring students to a good level of knowledge of the basic principles of modern physics. The student is expected to be able to apply mathematical techniques such as Fourier series and integrals to solving problems in modern physics .


Basic mathematics and physics of the first year and of the second semester of the second year.


Both the lessons and the exercises are carried out on the blackboard. Students are always invited to actively participate by asking questions, proposing solutions to the proposed problems. The active involvement of students probably contributes to reducing the time and difficulties related to the study of the topics presented in the course.


Modern physics, developed since the second half of the nineteenth century, has marked a conceptual leap in various respects with respect to classical physics. Its roots are in statistical thermodynamics and classical eletromagnetism, and more generally in classical wave theory. These themes constitute the first two parts of the course. The third part will cover quantum mechanics. The course will highlight not only the conceptual leap, but also the profound continuity that links these three important chapters of physics.

Statistical thermodynamics

Classical mechanics in phase space. Energy and the Hamilton function. Microscopic meaning of energy and entropy. Heat propagation, local energy conservation and Fourier equation. Boltzmann's Entropy. Statistical significance of the second law of thermodynamics. Ehrenfest model. Thermodynamic fluctuations and Einstein's formula. Probability rudiments: random variables, continuos and discrete distributions, mean value and variance, statistical independence. Random walk and introduction to the theory of Brownian motion. Gibbs distribution and calculation of average values ​​using the partition function; applications to the  ideal gas and systems with discrte energy levels. Boltzmann equipartition theorem and calculation of specific heats for poly-atomic gases and comparison with experimental data.

Classic waves

Free harmonic oscillations, normal modes. Propagation by waves of physical perturbations. Elastic waves in fluids. D'Alembert equation. Stationary waves and vibrating string. Helmholtz equation. Local conservation laws and continuity equation. Electromagnetic waves. Plane and spherical waves. Wave packets and Fourier analysis. Bandwidth theorem ("Heisenberg classical principle"). Dispersive media. Dispersion relations and wave equations.   Wave interference and coherence. The two-slit experiment. Diffraction. Fourier Optics. Principle of Fermat and of Huygens. Introduction to the special theory of relativity.

Quantum waves

Elements of crisis of the classical theories: black body, photoelectric effect. Electromagnetic field in a cavity as a set of independent oscillators. Einstein hypothesis E = h nu and determination of the Planck distribution. Stefan-Boltzmann law. De Broglie hypothesis mv = h / lambda and its experimental verification (from the Davidson and Germer experiment to recent experiments of interference of material waves). Minimum action principle and Fermat principle. Energy waves and matter waves. Basic concepts of quantum mechanics: wave equation in dispersive media and time-dependent Schroedinger equation, wave function and quantum state. Equation of continuity and probabilistic interpretation of the wave function. Uncertainty principle.  Correspondence rules. Classical Hamilton function and quantum Hamilton operator. Stationary states and the time-independent Schroedinger equation. Free states and bound states. Gaussian packets. Schroedinger equation with potential, study of some one-dimensional cases: wells, potential barriers and harmonic oscillator. Calculation of the average energy of a quantum harmonic oscillator in contact with a thermostat. The Schroedinger equation in three dimensions. Well of infinite cubic potential and the notion of degeneration of levels. The hydrogen atom: levels and quantum numbers. The Stern-Gerlach experiment and the spin. Quantum mechanics of multi-particle systems. Bosons and Fermions. Entanglement.



-  Chimica Fisica, Peter Atkins e Julio De Paula, (Zanichelli 2012);

- Introduction to Quantum Mechanics: David J. Griffiths (Benjamin Cumming, 2004);

- La fisica di Feynman, Volume 3. “Meccanica quantistica” (Zanichelli 2007);  available on-line  at


Exam Board



NICODEMO MAGNOLI (President Substitute)

PAOLO SOLINAS (Substitute)



The calendar of lessons is published in the 2021 Study Manifesto

Class schedule

L'orario di tutti gli insegnamenti è consultabile all'indirizzo EasyAcademy.



The exam consists of a written test and an interview. The written test consists of some problems that cover a large part of the course contents. The student is then given the freedom to choose between two types of oral: a shorter oral, aimed at consolidating the grade obtained in the written test, and a longer oral in which the change in grade can be significant. This modality is used to allow the student, aware of having achieved a good preparation, to be able to recover any shortcomings of the written test.


The written test is aimed at verifying the ability to solve specific problems similar to those discussed in the course, but original. The difficulty of the test is graduated, so that it is possible to separate the assessment of basic elementary knowledge, sufficient to pass the test, from the assessment of more advanced skills. Both in the short and in the long form of the oral one always starts from the written test, in order to ascertain the types of errors, the real mastery by the student of the skills required on the theory topics of the written test and highlight any lack of preparation. The long oral exam continues with the assessment of skills on other topics covered in the course. In both cases, the exam is aimed at ascertaining the degree of achievement of the training objectives, in a graded form. In both cases, particular attention is paid to ascertaining that the student has acquired a good level of knowledge of the basic principles of modern physics and that he is able to apply the mathematical techniques developed in the course to solve modern physics problems.