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 contemporary single-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.

Historical introduction: Black-body radiation, Photoelectric effect, Radiative collapse, Bohr’s atom. Two-slit experiment. Superposition principle. Two state systems: polaroid, spin, qubit. Schroedinger Equation for finite-dimensional systems. The problem of measurement. Structure of finite-dimensional Hilbert spaces. Dirac’s Notation. Self-adjointness and observables. Spectrum. Spectral theory, simultaneous diagonalization and compatible observables. Born’s rule. Collapse. Statistical mixtures, density matrix. Bell inequalities, locality, EPR, interpretation. Examples: quantum algorithms (Grover), quantum teleportation, quantum cryptography. Ininite-dimensional Hilbert spaces. Time-dependent and stationary Schroedinger Equation. Born’s rule and collapse for infinite-dimensional systems. Continuous spectrum Potential well, Dirac potential, Harmonic oscillator, Hydrogen atom. Creation and annihilation of particle: Fock spaces. Some examples from quantum electrodynamics and mean-field theories.

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

Notes from lectures (one every two weeks) and from exercise sessions. 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.

Lecture slides; Lecture notes;

Exam: Written test; Optional oral exam;

A written exam with two or three exercises on the programme of the course. Every exercise consists of three/four open questions. The duration of the written exam is three hours. The maximal grade is 30 cum laude. Upon request by the student or the teacher, an oral exam is delivered, with at least two questions on the programme of the course. In the oral exam, a first question has theoretical character, a second question consists in an exercise. Further questions can be addressed if needed to reach a precise definition of the grade.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.