CODE  66559 

ACADEMIC YEAR  2022/2023 
CREDITS 

SCIENTIFIC DISCIPLINARY SECTOR  FIS/02 
TEACHING LOCATION 

SEMESTER  Annual 
PREREQUISITES 
Propedeuticità in ingresso
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TEACHING MATERIALS  AULAWEB 
OVERVIEW
The course discusses the main experimental evidences that motivate abandoning classical mechanics to describe atomic physics. The fundamental principles of nonrelativistic quantum mechanics and its mathematical formalism are presented. Applications of quantum mechanics to the physics of particles, atoms, molecules, gases and condensed matter are described. In the second part of the course approximation methods and scattering theory are developed.
AIMS AND CONTENT
LEARNING OUTCOMES
At the end of this lecture course, the student will have developed a good understanding of quantum mechanics basic principles, as well as the theory's mathematical foundations. The student will be able to apply this knowledge to solve concrete problems involving physical phenomena at the atomic scale, both exactly and by using approximation methods
AIMS AND LEARNING OUTCOMES
At the end of these courses the student will be able to
 Identify the physical contexts which require a quantum description of the relevant phenomena;
 Compute the probabilities of simple quantum mechanical processes involving systems with finite number of states;
 Compute the tunnelling probabilities for potential barriers in one spatial dimension;
 Compute the spectrum of angular momentum (spin) operators for both simple and composed systems;
 Solve the Schrödinger equation for a system of two particles interacting with a central potential to compute the energy spectrum of hydrogen atom;
 Compute wave functions and energy spectra of systems composed by identical particles;
 Relate the laws of motion of classical mechanics to those of quantum mechanics, using both the WKB method, and the variational method;
 Calculate the timeindependent perturbation to the spectrum of a known Hamiltonian;
 Determine a transition amplitude by the theory of timedependent perturbations;
 Express the cross section in terms of a transition amplitude;
 Determine the density matrix for a given statistical mixture and use it to calculate an average value.
PREREQUISITES
PREREQUISITES
Basic knowledge of classical mechanics and analytical mechanics, mathematical analysis, geometry and linear algebra.
TEACHING METHODS
The course is delivered through frontal lectures that include
 Blackboard presentation
 Problems solved by the lecturers at the blackboard
 Problem solved by the students and discussed all together
SYLLABUS/CONTENT
Part A:
A1 The crisis of classical physics
1.1 Atomic models
1.2 Photoelectric effect and photons
1.3 Compton effect
1.4 Atomic absorption and emission spectra
A2 The old quantum theory
2.1 Bohr atomic model
2.2 De Broglie wavelength and waveparticle duality
2.3 BohrSommerfeld quantization rule
2.4 Davisson e Germer experiment
2.7 Particle interference
A3 The formalism of quantum mechanics
3.1 Superposition principle: states and vectors
3.2 Scalar products and transition probabilities
3.3 Observables, operators and eigenvector basis
3.4 Compatible and incompatible observables
3.5 Equivalent representations and unitary transformations
3.6 Quantum systems with finite basis
A4 Particle Quantum mechanics
4.1 Uncertainty relations
4.2 Canonical relations
4.3 Continuous spectrum: generalized eigenstates and observables
4.4 Coordinates and momenta representations
4.5 Wave packets
4.6 Schrödinger equation
A5 Temporal evolution
5.1 Schrödinger and Heisenberg pictures
5.2 Time evolution of a Gaussian packet
5.3 Continuity equation
5.4 Collective interpretation of the wave function
A6 Onedimensional Schrödinger equation
6.1 Free particle
6.2 Particle in a box
6.3 General properties of energy eigenfunctions in 1 dimension
6.4 Step potential
6.5 Square potential well
6.6 Potential barrier: transmission and reflection coefficients
6.7 Tunnel effect: semiclassical limit. Alpha decay
6.8 Harmonic oscillator: creation and destruction operators
A7 Symmetries
7.1 Translations and rotations
7.2 Discrete translations: Bloch theorem
7.3 Angular momentum and its representations
7.4 Spin
7.5 Addition of angular momenta
7.6 Scalar and vector operators
7.7 Harmonic polynomials and spherical harmonics
7.8 Schrödinger equation in central potential
7.9 The levels and the energy eigenfunctions of the hydrogenoides
A8 Atoms and Molecules
8.1 Fundamental level of Helium
8.2 Excited levels of Helium
8.3 Identical particles: bosons and fermions
8.4 Pauli principle
8.5 Zeeman effect
8.6 Hydrocarbons
Part B:
B.I: Advanced topics in QM (3 weeks)
1. Symmetries in Quantum Mechanics
2. Selection rules for scalar and vector operator. WignerEckhart theorem.
3. Mixedstates, density matrix
B.II: Approximation methods (4 weeks)
1. Timeindependent perturbation theory: degenerate and nondegenerate case.
2. Applications to hydrogenoids: fine and hyperfine structure, Zeeman effect.
3. Variational methods
4. WKB approximation
B.III: Timedependent Hamiltonians and Scattering (4 weeks)
1. Formal solution of the Schrodinger equation with timedependent hamiltonians. Dyson series. Exact solutions: spin resonance.
2. Timedependent perturbation theory. Interactions with classical radiation. The adiabatic approximation.
3. Elastic scattering: timedependent and timeindependent formalism. Lippmann Schwinger equation. Born approximation.
4. Partial waves expansion.
B.IV: Towards Relativistic Quantum Mechanics (1 week)
1. KleinGordon and Dirac equation.
RECOMMENDED READING/BIBLIOGRAPHY
 L. E. Picasso, "Lezioni di Meccanica Quantistica", (Edizioni ETS, Pisa, 2000)
 Richard Phillips Feynman, Robert B. Lieghton and Matthew Sands, "The Feynman Lectures on Physics", Vol 3 (Quantum Mechanics),(1966) (edizione online http://www.feynmanlectures.caltech.edu)
 L.D. Landau, E.M. Lifsits, vol. 3: "Meccanica Quantistica", Editori Riuniti
 Griffiths, Schroeter, “An introduction to Quantum Mechanics", 3rd edition
 Sakurai and Napolitano, “Modern Quantum Mechanics", 3rd edition
 S. Weinberg, "Lectures on Quantum mechanics", ed. Cambridge
TEACHERS AND EXAM BOARD
Ricevimento: Please schedule an appointment by email.
Ricevimento: Please schedule an appointment, in person or on Teams, by email. Camillo Imbimbo, Dipartimento di Fisica, Via Dodecaneso 33, 16146 Genova Office 717, Floor 7, phone: 0103536449 camillo.imbimbo@ge.infn.it
Exam Board
CAMILLO IMBIMBO (President)
STEFANO GIUSTO
NICOLA MAGGIORE
SIMONE MARZANI (President Substitute)
LESSONS
Class schedule
The timetable for this course is available here: Portale EasyAcademy
EXAMS
EXAM DESCRIPTION
The exam is made up a written test and an oral part. Rules and criteria and specified on the course aulaweb page.
ASSESSMENT METHODS
The written test has a duration of 4 hours and contains two problems, one for each part of the course. The problems are divided into questions of variable difficulty, in order to more accurately evaluate the level of competence achieved by the student.
The oral exam, which lasts about 40 minutes, is lead by two professors responsible for the two parts of the course. During the oral exam the student is asked to answer a few questions or to solve problems at the blackboard, in order to assess the student’s knowledge and understanding of the topic discussed. During the lectures, students will be given the opportunity to solve problems and exercises, as a means of selfevaluation.
Exam schedule
Data appello  Orario  Luogo  Degree type  Note 

11/01/2023  14:00  GENOVA  Scritto  
10/02/2023  14:00  GENOVA  Scritto  
05/06/2023  14:00  GENOVA  Scritto  
05/07/2023  14:00  GENOVA  Scritto  
11/09/2023  14:00  GENOVA  Scritto 