Introduction to Quantum Mechanics. Scroedinger equation. Hilbert spaces. Axioms of quantum mechanics, uncertainty principle. Tunnel effect. Hydrogen atom. The spin.
Introduction to special relativity. Axioms of special relativity. Relativistic kinematics. The structure of Minkowski space-time. The Lorentz and Poincare' groups. Relativistic
mechanics. Equivalence between mass and energy. Relativistic electrodynamics.
D. J. Griffiths, Introduzione alla meccanica quantistica, Ed. CEA.
A. Messiah, Quantum Mechanics, Ed. North-Holland.
C. Cohen-Tannoudji, B. Dui, F. Laloe, Quantum Mechanics, Ed. Wiley.
L. Debnath, P. Mikusinski, "Hilbert Spaces with Applications", Ed. Elsevier.
D. Colferai: Appunti di relativita' speciale.
C. Möller: The theory of relativity, Oxford at the Clarendon press.
W. Rindler: Essential relativity, special, general and cosmological, Springer-Verlag.
Learning Objectives
Knowlegde of basic concepts of quantum mechanics and special relativity.
Prerequisites
None.
Teaching Methods
CFU: 9
Contact hours for: Lectures (hours): 72
Type of Assessment
Oral test, about one hour long. The student will be asked to discuss 3-4 topics. Assessment: the student is required to use the appropriate language to show the comprehension of the basic physical processes, and how the outcomes depend on the assumptions. In order to determine the student's comprehension of the subject, further questions will be posed during the exposition. The student is required to be able to perform order-of-magnitude estimates of basic observableas, as well as detailed calculations employing the appropriate mathematical framework when necessary.
Course program
Introduction to Quantum Mechanics.
Classical physics crisis. Scroedinger equation, wave function, probability. Hilbert spaces and linear operators. Axioms of quantum mechanics, Heisenberg's uncertainty principle. One dimensional problems, tunnel effect. Quantization of angular momenta. Hydrogen atom. The spin. Entanglement. Interpretation and paradoxes of quantum mechanics.
Introduction to special relativity.
Axioms of newtonian mechanics, equations of electromagnetism. Axioms of special relativity. Relativistic kinematics. The structure of Minkowski space-time. The Lorentz and Poincare' groups. Tensor calculus. Relativistic mechanics. Equivalence between mass and energy. Relativistic electrodynamics.