Introduction to Nanoscience & Introduction to Quantum Physics

Aim of the Course

The course wants to give an overview to modern physics, starting from the crisis of classical physics to the establishment of quantum physics, nanoscience and nanotechnology. The main aim is to provide an introduction to quantum mechanics and the basic concepts to understand when and why quantum confinement effects dominate the properties of materials. Particular attention is given to the change of properties or arising of new phenomena when matter is confined at the nanoscale level. Topics discussion includes: fundamental concepts (wave-particle duality, wave function, uncertainty and exclusion principle), Schroedinger equation, quantum operators, stationary states, bound and unbound states, quantum statistics, density of states and some hints to atomic physics. 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 approaching advanced topics in atomic physics, nuclear physics, solid state physics, nanoscience and nanotechnology.

Learning objectives

At the end of the course the student should be able to understand some fundamental physical effects occurring when a system is confined to the nanoscale level and when quantum effects are dominant. Starting from basic concepts of quantum mechanics the student will develop the capability to analyze the physical behavior of free electrons in different potentials as models of low dimensional systems.

Programme at a glance

• 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
• Electron spin, many particle systems, Fermions and Bosons and occupation probability (Fermi-Dirac and Bose Einstein distributions), indistinguishability, exchange symmetry and Pauli principle.
• 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)
• Density of states in 0-D, 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 crsytal is performed in the classroom with portable equipment to show wave-particle duality.

Requested background

To attend the course the students are expected to know the fundamentals of classical physics (e.g. classical mechanics, conservation laws, wave mechanics, electromagnetism) and mathematics (e.g. vectors, complex numbers, differential operators, partial diferenttial equations).

The final examination consists in an oral discussion of the topics presented and discussed in the course lectures.

Two different topics will be discussed (about 30-45 minutes). The first topic is selected by the teacher, the second is at the student’s choice. Not answering to the first topic does not permit to discuss the second one. More information available on the course website in the BeeP portal.