The course aims to provide the basic mathematical tools and formalism necessary to obtain a quantum description of physical systems, and to discuss their application in predicting quantum phenomena, effects and properties characterizing systems such as the hydrogen and helium atoms, elementary molecule and matter-radiation models, the electromagnetic field, and systems of identical particles.

Students are expected 1) to achieve an effective understanding of the fundamental concepts and formal tools of Quantum Mechanics, 3) to develop ability in using them in the study of quantum systems, and 3) to develop a correct approach to the investigation of quantum systems. These achievements are certainly important for subsequent courses such as solid-state and condensed-matter physics, field theory, quantum statistical mechanics, nuclear physics.

The knowledge of differential calculus, linear algebra concepts, vector-space theory and matrix diagonalization is required as well as the knowledge of the principles, laws and theorems of classical Mecahnics and electromagnetism.

1) The Lagrangian and Hamiltonian approaches to classical mechanics. (0.5 cr) 2) The postulates of Quantum Theory. Time evolution of quantum systems. The Eherenfest theorem. The canonical-quantization scheme. (0.5 cr.) 3) The Hilbert space of quantum states. Scalar product, completeness relation. Properties of Hermitian operators and eigenvalue equations. (0.7 cr.) 4) Raising and lowering operators, solution of the harmonic-oscillator problem. The Heisenberg uncertainty relation. Coherent states and semiclassical picture of quantum systems. (0.6 cr). 5) Spectrum and eigenstates of the angular momentum. The two-body problem. The hydrogen atom. (1.0 cr.) 6) Dirac's formulation of quantum states and operators. The Schroedinger and Heisenberg representations of quantum Mechanics. (0.6 cr) 7) The spin operator and spin states. Addition of angular momenta. Time-independent perturbation theory. (0.7 cr) 8) Charged particles in the electromagnetic field. The Zeeman effect for Hydrogen atoms (weak and strong-field limit) (0.8 cr) 9) Symmetric and antisymmetric states of identical particles. Bosons, fermions and symmetrization principle. The exclusion principle. The Helium atom. (0.6 cr)

The teaching approach of this course is the traditional one based on frontal lectures. Each part of the program and the relevant calculations are discussed, step by step, and showed on the blackboard. As shown in the syllabus, the course is essentially divided in two sections: 1) Introduction to quantum physics, definition and/or derivation of the new formalism, methods and new theoretical tools necessary to develop the quantum-mechanical approach to physical systems, 2) study of various fundamental physical systems with the goal to achieve an effective modeling of such systems and to highlight their properties and significant physical effects. Exercise are proposed in the form of simple applications of the theory that each student must solve on his own. Solutions are provided in the subsequent lectures. Weekly meetings will be scheduled to give the students participating in this course the possibility to ask for questions, express doubts and clarify unclear points.

The PDF file containing the notes relevant to the course lectures are available in the web page of this course accessible through the Teaching Portal of Politecnico. Franz Schwabl , Quantum Mechanics, Springer-Verlag 2007 David J. Griffiths, Introduction to Quantum Mechanics, Addison-Wesley 2005;

Modalità di esame: Prova orale obbligatoria;

The exam is oral and consists of three questions concerning different topics of the course. Each question corresponds to a score of 10 out of 30 marks. The goal, in general, is to test the knowledge of the course program. These questions aim to evaluate the understanding of students concerning 1) the methodology used to quantize classical systems, 2) the significant properties and effects that characterize physical systems as a consequence of the quantization process and 3) the mathematical tools used to develop quantum mechanics. To this end one of the three question is focused on proving/discussing some theorem or general property characterizing quantum systems and the mathematical formalism of quantum mechanics. The other questions are devoted to discuss the quantization of physical systems for some specific case and/or to determine quantum effects and physical properties of interest emerging from this process. Oral exams based on the video-communication tools will take place according to the guide lines of the Decreto Rettorale n. 271, February 28, 2020.

Modalità di esame: Prova orale obbligatoria;

No blended exam are planned for the current course (Quantum Physics)