Elements of theoretical physics

Course objectives

Knowledge and ability to understand: The course aims to provide useful knowledge to understand some aspects of theoretical physics, and specifically of quantum mechanics and statistical mechanics. Particular attention will be dedicated to the analysis of the hypotheses founding the two disciplines. Through the study of these issues the student will be able to understand the evolution of physics that took place at the beginning of the last century, the impact they had on the development of society and their current importance. Ability to apply knowledge and understanding: The course is aimed at providing tools for the analysis and evaluation of physical phenomena on atomic scales and on the collective behaviors of large numbers of interacting particles. This knowledge can also be exported to fields other than those proposed in the course. Making judgments: Through the study of the theoretical approaches to quantum mechanics and statistics, the student will be able to improve his ability to interpret the real. Communication skills: The development of communication skills, mainly oral, will be stimulated through the discussion in the classroom and possibly with participation in seminar activities. Learning ability: The ability to learn will be stimulated through the discussion in the classroom, which will include interactive aspects also aimed at verifying the effective understanding of the topics covered. The learning capacity will also be stimulated by integrative teaching supports (original articles) in order to develop the application skills.

Channel 1
MARCO GRILLI Lecturers' profile

Program - Frequency - Exams

Course program
-- Introduction to Quantum Mechanics Short introduction to Hamilton formulation of classical mechanics Axioms of QM Free particles Free particle in an infinite potential well Potential barriers, tunnel effect Harmonic oscillator Angular momentum Spin Hydrogen atom -- Introduction to Statistical Mechanics Short recap of Thermodynamics The phase space, time averages Statistical ensembles Microcanonical, canonical, and grand canonical ensembles Partition function and free energy Relations between thermodynamical and statistical quantities Quantum statistical mechanics Fermi-Dirac and Bose-Einstein distribution functions Bose condensation
Prerequisites
Knowledge inherent in the bachelor's degree in mathematics. In particular, elements of classical mechanics and electromagnetism, Lagrangian and Hamiltonian formulation of classical mechanics, basics of probability theory, calculus and geometry.
Books
Prof. Sciortino's Lecture notes Quantum Mechanics (1) di Claude Cohen-Tannoudji, B. Dui, Franck Laloe Wiley ed. For some specific topics in QM I also suggest: Feynman, Leighton, Sands https://www.feynmanlectures.caltech.edu/III_toc.html Chapter 1 Statistical Mechanics di Kerson Huang Wiley ed.
MARCO GRILLI Lecturers' profile

Program - Frequency - Exams

Course program
-- Introduction to Quantum Mechanics Short introduction to Hamilton formulation of classical mechanics Axioms of QM Free particles Free particle in an infinite potential well Potential barriers, tunnel effect Harmonic oscillator Angular momentum Spin Hydrogen atom -- Introduction to Statistical Mechanics Short recap of Thermodynamics The phase space, time averages Statistical ensembles Microcanonical, canonical, and grand canonical ensembles Partition function and free energy Relations between thermodynamical and statistical quantities Quantum statistical mechanics Fermi-Dirac and Bose-Einstein distribution functions Bose condensation
Prerequisites
Knowledge inherent in the bachelor's degree in mathematics. In particular, elements of classical mechanics and electromagnetism, Lagrangian and Hamiltonian formulation of classical mechanics, basics of probability theory, calculus and geometry.
Books
Prof. Sciortino's Lecture notes Quantum Mechanics (1) di Claude Cohen-Tannoudji, B. Dui, Franck Laloe Wiley ed. For some specific topics in QM I also suggest: Feynman, Leighton, Sands https://www.feynmanlectures.caltech.edu/III_toc.html Chapter 1 Statistical Mechanics di Kerson Huang Wiley ed.
  • Lesson code10589497
  • Academic year2025/2026
  • CourseMathematics
  • CurriculumAlgebra e Geometria
  • Year1st year
  • Semester1st semester
  • SSDFIS/02
  • CFU6