- Docente: Francesco Ravanini
- Credits: 7
- SSD: FIS/02
- Language: Italian
- Moduli: Francesco Ravanini (Modulo 1) Sandro Turrini (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Atmospheric physics and Meteorology (cod. 8008)
Learning outcomes
At the end of the course the student: - knows the limits of classical physics and the experiments that point to them; - knows the general structure of wave mechanics and operatorial methods in quantum mechanics; - knows the Schroedinger equation in 3 dimensions and the hydrogen atom solution; - is able to use variational methods and time-independent perturbation theory to solve some basic problems.
Course contents
Crisis of Classical Mechanics and beginning of Quantum
Mechanics - Wave and particle theories of light - Photoelectric
Effect, Compton Effect. - Bohr quantization, Bohr atom. -
Interference experiments: wave-particle duality. - De Broglie
hypotesis and wave function. - Schrödinger Equation for the time
evolution.
Mathematical Formalism - Hilbert spaces, linear operators,
eigenstates and eigenvalues. - Commutativity. - Complete sets of
eigenstates. - Eigenfunction expansion. - Square summable
functional spaces. - Orthogonal Polinomials. - Series and Fourier
transforms. - Distribution Theory.
General Principles of Quantum Mechanics - Postulates. -
Eigenvalue problem for the Hamiltonian. - Measure theory and
development in eigenstates. - Mean Values. Ehrernfest theorem. -
Position-momentum commutation rules. - Heisenberg Indetermination
relations. - Fourier transform and momentum representation.
1D Problems - Parity. - Harmonic Oscillator: polynomial and à la
Dirac solutions. - Potential wells. - Potential barriers, tunnel
effect. - Delta Potential.
Approximate Methods - Time independent perturbation theory,
non-degenerate case: first and second orders; degenerate case -
Time dependent perturbation theory. - Variational methods.
Symmetries - Symmetries, infinitesimal transformations
and their generators. - Translations and momentum. Rotations and
angular momentum. - Parity.
Angular momenta - 3D spatial rotations and angular momentum
in QM, its eigenvalues and eigenvectors. - Parity and angular
momentum. - Complete sets of commuting operators -
Half-integer eigenvalues and electron spin - Pauli matrices
algebra - Combination of angular momenta.
Central symmetry problems - Central potentials. - Azimutal
and accidental degenrations. - Coulomb problem (hydrogen atom
without spin) - Links with Bohr atom - Stark-LoSurdo effect - 3D
isotropic harmonic oscillator.
Identical particles and statistics - Bosons and fermions -
Pauli Exclusion principle.
Interaction of an electron with the electromagnetic field -
Normal and anomalous Zeeman effect - Supplementary terms in the
Hydrogen atom hamiltonian. - Fine and hyperfine structures of the
hydrogen atom.
Readings/Bibliography
Notes of the course are available onAMS Campus.
For the written exam preparation, the student is strongly
encouraged to see the exam problems of the past years, also present
onAMS Campus
Other books suitable for deepening some specific arguments:
* Cohen-Tannoudji C., Diu B., Laloe F. - Mécanique Quantique -
Dounod (in French) - Quantum mechanics, - Wiley Ed. (in English)
* Galindo Pascual, Mecanica Cuantica (in Spanish) Eudema (Madrid)
* L.D. Landau, E.M. Lifshitz - Theoretical Physics vol.3: Quantum
Mechanics, Non-relativistic Theory - MIR Eds.
* J. Chahoud, Meccanica Quantistica (in Italian) - Ed. Pitagora
Teaching methods
* Lectures at the blackboard and with projection of transparencies,
with the participation of students.
* Exercises solved together with the students with
comments.
* Further exercises proposed as homework with correction in
the class. Although not compulsory, they may reveal crucial for the
preparation of the written exam.
Assessment methods
Written Exam:
* time: 3 hours.
* from one to four problems for a total of about 8
questions.
* sheets for scketchy calculations etc... will be provided, not to
be given back at the end. Only the offical copy, possibly ordered
and well commented will be given. * any text, notes etc...
can be used without restriction.
* the result of the proof has 14 months validity.
Oral Exam:
* can be done only in presence of a positively evaluated written
exam
* 3 questions chosen by the teachert
* the final score is (approximatively) an average between the
written and oral results.
Teaching tools
The "Avvisi" section of the teacher website will be used for
commuincations.
The learning material will be made available on the AMS Campus
website.
Office hours
See the website of Francesco Ravanini
See the website of Sandro Turrini