The first part of the course aim at providing the basic concepts of quantum mechanics, exemplified through simple applications, such as the particle in a box model, the quantum harmonic oscillator and the hydrogen atom. In the second part of the course, the laws of quantum mechanics will be applied to describing the properties of crystalline solids. In particular, the student will learn how the band structure and the density of states influence the electronic and optical properties of solids.

The students are expected to learn the principles of quantum mechanics and apply them to simple model systems and to condensed matter structures. Main anticipated achievements are: - Knowledge of the postulate of quantum mechanics and their application to simple model systems - Knowledge of quantum statistical distributions and their applications - Knowledge of electronic and optical properties of solids - Ability to solve the Schrodinger equation for simple model systems - Ability to interpret the band structures, density of states and phonon dispersion curves of crystalline solids - Ability to use quantum physics-based models for the prediction of materials properties.

Classical Physics. Differential calculus and linear algebra.

- From classical physics to quantum mechanics. (2 hours) - The postulate of quantum mechanics. Physical observables and Hermitian operators in quantum mechanics. Commutators and the Heisenberg indetermination principle. (8 hours) - Solution of the Schrödinger’s equation for simple one-dimensional quantum problems. (6 hours) - The quantum harmonic oscillator (raising and lowering operators). (3 hours) - Spectrum and eigenstates of the angular momentum. The hydrogen atom. (6 hours) - The spin operator and spin states. (1,5 hours) - Introduction to the Bose-Einstein's and the Fermi-Dirac's distribution. (4 hours) - Crystalline and amorphous materials. Direct and reciprocal lattice. (4,5 hours) - Electrons in solids: the Sommerfeld model, Bloch theorem, bands, and Fermi surfaces. (9 hours) - Electronic properties of metals and semiconductors. Doping of semiconductors. (6 hours) - Phonons in condensed matter. (5 hours) - Photon-matter interaction. (5 hours)

The course consists of theoretical lectures and class practices. The latter include simple problem-solving activities and small computer program coding, with strict connections to theoretical lectures.

D. J. Griffiths, “Introduction to Quantum Mechanics” (Addison-Wesley). H. Ibach and H. Luth, "Solid-State Physics: An Introduction to Theory and Experiment" (Springer). N. W. Ashcroft and N. D. Mermin, "Solid state physics" (Brooks Cole). C. Kittel, "Introduction to Solid State Physics" (Wiley). Lectures notes produced by the teacher will be available on-line at the course web page.

Slides;

Modalità di esame: Prova scritta (in aula); Prova orale facoltativa;

Exam: Written test; Optional oral exam;

... The exam consists of a written test aiming at addressing the degree of understanding achieved by the students on the subjects explained during the lectures (see expected learning outcome above). The exam aims at assessing the comprehension of quantum physics and condensed matter phenomena. No supporting material is allowed during the exam. When writing the exam sheet the student has to show that he/she is able to rigorously discuss and present the physical models introduced during the lectures. The written test includes multiple-answer questions, statements (to be assessed as true or false) and two open questions covering all the course’s subjects. The maximum mark for questions/statements is 12/30, that of the open questions is 18/30. The total allotted time is 90 min. An oral exam, for students who passed the written test is possible although not compulsory.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.