Mathematics

General targets: acquire basic specialist knowledge on some classic topics of Physics-Mathematics. Knowledge and understanding: knowledge of the theory of compact self-adjoint operators, of the applications of this theory to the theory of potential; basic knowledge of Hamiltonian Mechanics and of Quantum Mechanics. Applying knowledge and understanding: the student will be able to analyze the spectrum of operators, also for unbounbed operators; to determine the eigenvalues of the Laplacian in domains with symmetries; translate into Hamiltonian formalism the Lagrangian problems and solve them for quadatrure; discuss the solution of the Schroedinger equation in simple but physically significant cases. To develop these aspects, in the course they are assigned and carried out appropriate exercises, subject to written verification. Making judgements: ability to enucleate the most significant aspects of the potential theory and of the theory of motion, ability to reflect on similarities and differences between the classical case and the quantum one. Communication skills: ability to enucleate the significant points of the theory, to know how to illustrate the most interesting parts with appropriate examples, to discuss mathematically the most subtle points. Learning skills: the acquired knowledge will allow the student to face the mathematical-physcs courses on more specialized subjects, and will allow the student to understand, even independently, the physical relevance of mathematical questions discussed in other courses.