The course aims at giving students the fundamentals of quantum and solid state physics, necessary for a microscopic description of the behaviour of matter and for understanding the manifestation of new phenomena at the micro and nano-scale, as those involved in micro and nano-systems.

Starting from classical electromagnetism (Maxwell equations, electromagnetic waves), students will realize the crisis of the classical physics in the 1900s (black body radiation, photoelectric effect,…) and will learn the fundamental concepts of quantum mechanics (wave-particle dualism, operators and observables, Schroedinger equation, Heisenberg uncertainty principle) and their application to the comprehension of atomic and condensed matter phenomena.

Finally, the quantum theory of solid state physics will be introduced (crystals and symmetry; Bloch's theorem; band structure), with a glance on electric properties of solids.

Knowledge and understanding (DD1): The student knows the fundamentals of classical electromagnetism and quantum mechanics applied to atoms and solid state. The student understands the need for a revision of the classical descriptive apparatus, with the introduction of new concepts and methods.

Ability to apply knowledge and understanding (DD2): The student is able to use the new concepts to set up the quantum description of a specific system and to apply these concepts to the quantitative description of physical phenomena at the microscopic level, using an adequate formalism and the competence in the use of specialized vocabulary.

Making judgments (DD3): The student is able of critical reasoning in the face of a physical problem, organizing the solution in a linear, logical, and effective way, understanding how classical physics constitutes a limiting case of quantum physics and when and why the quantum description can be reduced to the classical one.

Learning skills (DD5): The student learns how to link the macroscopical physical properties of a system with its microscopic quantum description.

The course is divided into three modules: starting from classical electromagnetism (module 1), students will realize the crisis of the classical physics and will learn the fundamental concepts of quantum mechanics and their application to the comprehension of atomic and condensed matter phenomena (module 2). Finally, quantum mechanics will be applied to solid state introducing the quantum theory of solid state physics, with a glance on electric properties of solids (module 3).

The rigorous theoretical approach, needed to access a quantitative description of physical phenomena using an adequate formalism, will be complemented by the solution of simple exercises and the discussion of focused applications of the arguments presented.

The program is structured as follows:

1. Classical electromagnetism:

- Maxwell equations for electric and magnetic fields: Faraday-Neumann-Lenz law, Ampère-Maxwell law, Poynting’s theorem

- Electromagnetic waves: general properties, complex representation, interference

2. Fundamentals of quantum mechanics:

- Crisis of the classical physics: black body radiation, photoelectric effect

- Wave-particle duality: photons, De Broglie wavelength

- Schröedinger equation: wave function and operators, stationary states, expectation values

- Examples: particle in a box, potential well, harmonic oscillator, tunnel effect

- Operators and observables: Hermitian operators, uncertainty principle, Ehrenfest’s theorem

- Hydrogen Atom: Bohr’s atom, quantum numbers, angular momentum

- Perturbation theory: transition probability

- Spin: Pauli exclusion principle, many electron atoms

3. Introduction to solid-state physics:

- Fundamentals of quantum theory of crystals: crystal lattice, electronic bands, Bloch’s theorem

- Electric properties: effective mass and holes, thermal excitation

The course makes extensive use of concepts and methods of classical physical. A good knowledge of the fundamental concepts of mechanics, electrostatics and magnetostatics is required.

As far as mathematical knowledge is concerned, a good familiarity with complex numbers, linear algebra and differential and integral calculus is needed.

The evaluation aims at verifying the knowledge and the understanding of the course topics, and the ability to apply critically this general knowledge to the description of electromagnetic phenomena and quantum systems, such as atoms and simple crystal structures.

The evaluation can be taken in one of the sessions established by the School calendar, and consists of a written test and an oral test. During the written test the use of books and/or notes is not allowed. The test is on paper. The written test is selective: if not passed, the student must repeat the exam.

The oral exam starts from the discussion of the written exam (if passed) and aims at ascertaining the degree of understanding of the topics included in the course program. The outcome of the oral test can be either better or worse than the outcome of the written test.

One of the many existing books on classical electromagnetism (from electrostatics and magnetostatics to Maxwell equations, electromagnetic waves)