The course is intended to give an overview of modern physics, starting from the crisis of classical physics to the establishment of quantum physics, nanoscience and nanotechnology. The main aim is to provide the concepts and the fundamental tools to understand when and why quantum confinement effects dominate the properties of materials. To understand the physical background of nanoscience and nanotechnology, particular attention is given to the change of properties and arising of new phenomena when electrons are confined at the nanoscale. The introductory but not elementary approach to quantum mechanics is calculus based and is intended to give the fundamental mathematical and physical tools needed for understanding the properties of materials and for approaching advanced topics in atomic physics, nuclear physics, solid state physics, nanoscience and nanotechnology.

After the course and a positive evaluation in the finale exam the student:

- knows the theory and the principles of quantum physics needed to describe the behavior of quantum particles (including the value of the main physical constants used in the course) and understand the difference between classical physics and some peculiar physical effects, that occur when quantum effects are dominant. 

- knows the classes of nanostructures, in particular carbon nanostructures as well as the working principle of scanning probe microscopy.

- is able to apply the mathematical tools of quantum physics to analyze and describe, in details, the stationary states of independent electrons in simple potentials as models of quantum confinement in low dimensional systems.

- is able to discuss in a logical way, adopting an appropriate and scientifically correct language.  

• What is nanoscience? (from Feynman's talk to nanotechnology)
• The crisis of classical physics and foundations of modern physics. The blackbody radiation and the photoelectric effect.
• Principles of Quantum Mechanics: uncertainty principle, electron wave function, probability density, Schroedinger’s equation, stationary and non-stationary states, wave packets, quantum operators and expectation values.
• Barrier penetration and tunnelling effect
• Models of confined systems: free electrons in a box with different dimensionality (1-D and 3-D) and size dependent properties.
• Electron in a central potential (atomic model)
• Electron spin, many particle systems, Fermions and Bosons and occupation probability (Fermi-Dirac and Bose Einstein distributions), indistinguishability, exchange symmetry and Pauli principle.
• Density of states in 1-D, 2-D and in 3-D systems.
• Introduction to scanning probe microscopy (atomic force microscopy and scanning tunneling microscopy).
• Introduction to carbon nanostructures (fullerenes and nanotubes). 

Laboratory activity

Experimental demonstration of diffraction of light by a grating and diffraction of electrons by a crystal is performed in the classroom with portable equipment to show wave-particle duality.

Mathematics and physics at Bachelor level in science and engineering disciplines is needed to follow the course. In particular the following knowledge is strongly requested to understand the course topics:

• Mathematics: complex numbers, functions behavior, trigonometric functions, vectorial calculus, differential calculus, derivatives, integrals, differential equations.
• Classical mechanics: kinetic and potential energy, particle motion and Newton's laws, momentum, angular momentum, wave kinematics (frequency, wavelength, amplitude).
• Fundamentals in classical electromagnetism: electrostatics, magnetostatics, electric charge, electric current, potential, Coulomb force, electric and magnetic fields.

The final examination will consist in an oral discussion of the course topics. Two different topics will be discussed (about 30 minutes). The first topic is selected by the teacher (after asking the student's choice), the second is at the student's choice. The student will have a paper sheet and a pen to write formulas and to draw graphs, schemes and whatever can support the discussion. Discussing not properly the first topic does not permit to discuss the second one. Understanding the physics underlying the mathematical approach is considered a fundamental aspect.

The examination is intended to verify that the student:

- knows the topics and understands the related hypotheses, the critical points, the mathematical approach and the physical constrains and consequences. 

- knows the approximate value and dimension of the main physical constants used in the course, has familiarity with values or order of magnitude and related dimensions of physical quantities.

- is able to apply the concepts and the tools of quantum physics to discuss the behavior of a system of independent electrons.

- is able to discuss the topics in a clear and synthetic way with a logical organization of the content and using an appropriate and scientifically correct language