Foundations of physics

A.Y. 2021/2022
6
Max ECTS
42
Overall hours
SSD
FIS/02
Language
Italian
Learning objectives
The course intends to carry out a historical-critical study of some central passages of the evolution that led to the development of quantum physics. It also intends to accustom the student to the direct reading of the original works of the great classics, thus complementing the traditional training, which is necessarily based on textbook . Finally, we want to illustrate recent studies based on new results in the theory of dynamic systems, which bring new light to some of the
critical passages in the development of quantum physics.
Expected learning outcomes
At the end of the course the student will

1) have understood the problem of the equipartition principle in classical statistics mechanics in connection with the theory of specific heats
2)have learned the basic phenomenological aspects of the black body radiation problem and read Planck's papers of 1900.
3) read Einstein's memory of 1905 on photons, and that of 1912 on the specific heats of solids.
4) have learned the basic phenomenological aspects of the emission spectra in gases.
5) have read Heisenberg's memory of July 1295 on the mechanics of matrices.
6) have understood the passage, invented by Schroedinger, from classical mechanics to wave mechanics, like the analog of the transition between geometrical and wave optics.
7) have read the memory of Einstein, Podolsky and Rosen, on the problem of the completeness of quantum mechanics
8) have read Bell's work on the inequality that bears his name.
Course syllabus and organization

Single session

Responsible
Lesson period
Second semester
The course will be delivered entirely remotely in case of restrictions due to Covid-19. The lectures will be offered in virtual classrooms (zoom platform) in synchronous connection.
Course syllabus
1) The problems of the black body radiation and of the specific heat. Reading and discussion of the Planck's papers on the black body radiation. Einstein interpretation in terms of energy fluctuations (1909 paper and Solvay conference in 1912). Relation with the specific heat problem: reading and discussion of the Einstein papers (1906, 1917). Relations with some recent research paper on the dynamical foundations of statistical mechanics ( the problem of the long thermalization time: from Boltzman to Fermi Pasta Ulam model to glasses phenomenology). The relevance of the Fluctuation Dissipation theorem (with a mathematical proof) for a deduction of the second principle (of Thermodynamic) in microscopic term.

2) The problem of atomic stability, from Bohr to Bohr-Sommerfeld theory. Action-angle variables. Relation with the problem of matter radiation interaction, and some outlines of some recent research work, from Wheeler Feynman identity to the infrared spectrum of ionic crystal.

3) Reading of the first 1925 Heisenberg work on matrix mechanics and of the 1926 Schroedinger works on wave mechanics. Born's interpretation. Nelson and Bohm approaches: comments.

4) Einstein Podolsky Rosen paradox. Reading of the original paper, of the Bohr's critique, and of the final replay of Einstein. Bell's paper on his inequality. Some experimental results.
Prerequisites for admission
Elementary notions of thermodynamics: temperature, heat, specific heat, internal energy and entropy.
Elementary notion of quantum mechanics: Schroedinger equation, energy level, spectral lines, quantum observables.
Teaching methods
Two different modality: traditional frontal lectures which are preliminary to the reading of a classic paper to be held in classroom.
Teaching Resources
Lecture notes: A. Carati, L. Galgani, "Progress along the lines of the Einstein classical program", downloadable from internet.
Reprints of al papers read and discussed in classroom are downloadable at the website
users.mat.unimi.it/users/galgan
Assessment methods and Criteria
The examination consists in an oral test which focuses on the program topics, in order to ascertain the student understanding both the technical aspects of the theories, and the scientific papers illustrated during the lectures.
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 6
Lessons: 42 hours
Professor: Carati Andrea
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Professor(s)