The course gives a presentation of Quantum Mechanics together with the necessary mathematical tools, from finite dimensional linear algebra to Fock Spaces. Example and applications are numerous and developed, aiming at applications on quantum computing, cryptography, teleportation, information.

Knowledge: basics of quantum mechanics mastering the mathematical formalism at a rigorous level; interpretation of quantum mechanics and related contemporary debate; applications to devices, from transistors to contemprary sigle-particle technology. Skills: solving problems on spectra of quantum observables, probability transitions, from spin systems to atomic systems. Write down quantum mechanical models for simple systems and discuss them. Reading autonomously classics of quantum mechanics as well as modern treatises.

Linear algebra, matrices, unitary and hermitian transformations. Diagonalization, quadratic forms, spectral theorem for finite-dimensional spaces.

Two-slit experiment. Superposition principle. Two state systems: polaroid, spin, qubit. The problem of measurement. Structure of finite-dimensional Hilbert spaces. Self-adjointness and observable. Spectrum. Spectral theory, simultaneous diagonalization and compatible observable. Collapse. Statistical mixtures, density matrix. Bell inequalities, locality, EPR, interpretation. Examples: quantum algorithms (Grover), quantum teleportation, quantum cryptography. Ininite-dimensional Hilbert spaces. Potential well, Dirac potential, Harmonic oscillator, Hydrogen atom. Creation and annihilation of particle: Fock spaces. Some examples from quantum electrodynamics.

Blackboard lectures and slides, with exercises. Participation and interaction is strongly encouraged.

Luigi E. Picasso, “Lectures in Quantum Mechanics”, Springer 2015 Luigi E. Picasso, E. d’Emilio, “Problems in Quantum Mechanics with Solutions”, Springer 2015. Griffiths, Schoeter, “Introduction to Quantum Mechanics”, 1995 Preskill, Lecture Notes on Quantum Information and Computation, online.

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

Exam: Written test; Optional oral exam;

... Written exercises on the programme of the course, with a possible oral integration

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.