Course Unit Page

Teacher Roberto Zucchini

Learning modules Roberto Zucchini (Modulo 1)
Francisco Manuel Soares Verissimo Gil Pedro (Modulo 2)

Credits 12

SSD FIS/02

Teaching Mode Traditional lectures (Modulo 1)
Traditional lectures (Modulo 2)

Language Italian

Teaching Material

Course Timetable from Sep 26, 2017 to May 31, 2018
Course Timetable from Mar 01, 2018 to May 22, 2018
Academic Year 2017/2018
Learning outcomes
At the end of the course, the student has the basic knowledge of the foundations, theory and applications of quantum mechanics, in particular the Schroedinger equation and its methods of resolution.
Course contents
Module 1
1) From classical physics to quantum physics
Undulatory theory of light, interference and diffraction
Photoelectric effect and Compton effect
Corpuscular theory of light
Material waves and de Broglie theory
Wave particle duality
Experience of Davisson and Germer
Atomic spectra
Experience of Franck and Hertz
BohrSommerfeld atomic model
Correspondence principle
Experience of Stern and Gerlach
Angular momentum and spin in quantum physics
Spatial quantisation
2) The Schroedinger equation
The wave equation and geometric optics
HamiltonJacobi equation and its relation to geometric optics
Quasiclassical limit
Derivation of the Schroedinger equation
Wave function and its probabilistic interpretation
Energy eigenfunctions and levels
Time evolution of the wave function
Schroedinger equation for a particle with spin
3) Solution of the Schroedinger equation
Schroedinger equation in one dimension
Energy eigenfunctions and levels
Potential boxes and wells
The onedimensional harmonic oscillator
Schroedinger equation in three dimensions
Schroedinger equation for a central potential
Orbital angular momentum, parity and spherical harmonics
Radial eigenfunctions
Spherical sotential boxes and wells
The hydrogen atom
Other examples and applications
4) Collision theory
Collision in quantum physics
Scattering in one dimension
Reflection and transmission coefficients
Potential barriers
Scattering in three dimensions
Differential and total scattering cross section
Scattering in a central potential
Born approximation
Partial waves expansion
Coulomb scattering
Examples and applications
5) Foundations of quantum physics
Basic quantum experiences
States, observables and measurement
Definition and eigenstates
Measurement and state reduction
Probabilistic nature of quantum physics
Spectrum of an observable
Superposition and completeness
Expectation values and uncertainty of an observable
Compatible observables and simultaneous eigenstates
Indetermination principle
6) Formalism of quantum mechanics
Bras, kets and orthonormal bases
Selfadjoint operators and eigenkets and eigenvalues of selfadjoint operators
States and kets
Observables and selfadjoint operators
Schroedinger, momentum and Heisenberg representations
Quantisation and canonical commutation relations
Ehrenfest theorem and quasiclassical limit
7) Elementary applications
Equazione di Schroedinger for a particle in an electromagnetic field
Twostate systems
The harmonic oscillator in the operator formalism
Other examples and applications
8) Angular momentum theory
Angular momentum commutation relations
Angular momentum spectral theory
Sum of angular momenta and ClebshGordan coefficients
WignerEckart theory
The hydrogen atom in the operator formalism
Pauli Theory of the spinning electron
9) Identical particles
Identity and quantum indistinguishability
Spin and statistics, bosons and fermions
Pauli exclusion principle
10) Time independent perturbation theory
Perturbations and lift of degeneracy
Non degenerate and degenerate perturbation theory
Perturbative expansion
Examples and applications
11) Time dependent perturbation theory
Schroedinger equation and evolution operator
Time dependent perturbations
Schroedinger, Heisenberg and Dirac representation
Pulse perturbations
Periodic perturbations
Fermi golden rule
Adiabatic approximation
Examples and applications
Module 2
Problem solving in the following topics of the course
Hydrogenlike atoms
Harmonic oscillator
Onedimensional potentials
Spin
Perturbation theory
Readings/Bibliography
P. A.M. Dirac
The Principles of Quantum Mechanics
Oxford University
Press
C. CohenTannoudji, B. Diu & F.
Laloe
Quantum Mechanics
I & II
WileyInterscience
J. J. Sakurai & J.
Napolitano
Modern Quantum Mechanics
AddisonWesley
A. Galindo & P.
Pascual
Quantum Mechanics
I & II
SpringerVerlag
L. D. Landau, E. M.
Lifshitz
Quantum Mechanics: NonRelativistic Theory
Elsevier
Teaching methods
Classroom lectures on a blackboard or with the help of a projector
Classroom problem solving on a blackboard.
Assessment methods
The exam includes a written part with theory questions and problems about the course contents and a oral one consisting in a discussion of the results of the written part. The grade obtained by the student and determined by the score obtained in the written part possibly modified in the oral part. The written and oral part of the exam must mandatorily be taken during the same session.
There are no prerequisites for admission to the exam and there is no minimum score of the written part required for accessing the oral part. There is no a separate exam for the recitation module.
The exam can be taken in two ways:
1) a partial examination on the first half of the program at midcourse followed by a partial examination on the second half of the program from the end of the course on;
2) an examination on the whole program from the end of the course on.
Only students enrolled in the third year in the current academic year may attend the partial examination. One can not take a partial exam on the first half of program after the end of the course.
As a rule, the student may repeat the examination at a second exam session if the grade obtained at the first one does not satisfy him/her within the same academic year. In that case, the grade obtained at the second attempt will be registered even if it is lower than that gotten at the first. The student can accept a grade he/she previously rejected within the academic year during which the grade was obtained. Over that term, the grade is canceled and the student must repeat the exam.
The student's grade takes into account not only his/her knowledge of the subject matter but also his/her ability of critical analysis and independent learning and the appropriateness of verbal expression.
The award of a cum laude grade is taken into account only for the student who has demonstrated an uncommon clarity of thought in the exposition of theory and virtuosity in the solution of problems in the written exam and after an additional oral exam on all the course contents confirming that the student possesses a degree of knowledge of the subject matter far above the average.
The total written exam comprises four themes, I  IV, divided into two parts: a, a theory question, and b, a problem.
The examining student is required to carry out two a parts and two b parts. chosen in the four themes. It is not necessary for a and b parts to belong to same theme.
The a and b parts can get a maximum score of 15/90 and 30/90, respectively. The maximum score the student can get in the written exam is therefore 90/90.
If more than two a or b parts are performed by the examining student, only the two where the student has achieved the highest score will be counted.
The total exam is three hours long.
The first partial written exam comprisess two themes, I, II, divided into two parts: a, a theory question, and b, a problem.
The examining student is required to carry out one a part and one b part chosen in the two themes. It is not necessary for the a and b parts to belong to same theme.
The a and b parts can get a maximum score of 15/90 and 30/90, respectively. The maximum score the student can get in the first partial written exam is therefore 45/90.
If more than one a or b part is performed by the examining student, only the one where the student has achieved the highest score will be counted.
The second partial written exam comprises two themes, III, IV, divided into two parts: a, a theory question, and b, a problem and has arugulation similar to that of the first partial.
Each of the two partial exams is one hour and thirty minutes long.
The written exam sheets must be numbered sequentially and carry the name of the examining student written in bold and legible. Sheets that do not meet these requirements will not be evaluated.
The teacher does not answer any question about the content of the examination.
Use of any form of documental material is prohibited. It's forbidden to copy from the sheets of other students. The breaching student will be automatically excluded from the examination.
The examination will be considered as taken by the student only if he/she hands the exam sheets for the correction. Delivery is not mandatory.
Delivery of the exam sheets will be accepted only upon exhibition of a valid identification document by the examining student.
Teaching tools
The following educational material is available on the AMS Campus web site
1) Lectute notes in English
2) Texts of the problems proposed in the problem solving classes with solutions in Italian
3) Texts of past written exams
Office hours
See the website of Roberto Zucchini
See the website of Francisco Manuel Soares Verissimo Gil Pedro