ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 99 Hours of tutorials: 3 Expository Class: 24 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Particle Physics
Areas: Theoretical Physics
Center Faculty of Physics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable
A solid understanding of the principles of quantum mechanics, its
mathematical formalism and its applications to various fields of physics.
LEARNING OUTCOMES
With respect to Quantum Physics II, the student will demonstrate:
Acquire a basic understanding of the principles, ability to solve basic practical problems and knowledge of the most important systems.
-Chapter 1: Review of some concepts of classical mechanics
-Chapter 2: The mathematical apparatus of quantum mechanics. Hilbert spaces.
Dual spaces and Dirac notation. Linear operators. Hermitian conjugation.
Unitary operators. Projectors. Eigenvectors and eigenvalues. Functions of
operators. Pauli matrices and the SU(2) group.
-Chapter 3: The principles of quantum mechanics. The postulates of Quantum
mechanics and its consequences. Temporal evolution. Ehrenfest
theorem. Heisenberg inequality. Two-level systems: Rabbi
oscillations. Particles of spin 1/2: dynamics and evolution over time.
-Chapter 4: Quantum Entanglement. Compounds Systems: tensor product and
entangled states. Density matrix. EPR paradox. Bell's inequalities.
Introduction to quantum information theory.
-Chapter 5: Wave Mechanics. Hilbert spaces of infinite dimension.
The position representation and the wave function. Spatial traslations
and the momentum operator. Eigenfunctions of the position and momentum
operators: plane waves. p-Representation. Schrodinger equation. Time evolution
of a free particle: wave packets. Stationary states. Current probability.
Principles of wave mechanics.
-Chapter 6: Simple systems: One-dimensional quantum systems.
Harmonic oscillator: creation and annihilation operators and energy levels.
Particle in an electromagnetic field: gauge invariance and
Aharonov-Bohm effect . Landau levels.
-Chapter 7: Angular momentum: Rotations. Representation theory of the
angular momentum. Rotation matrices. Application to the study of a particle
in a central field. Addition of angular momenta.
-Chapter 8: Approximate Methods. Theory of time independent perturbations.
Time dependent perturbations: transitions and
Fermi golden rule. Semiclassical approximation. Variational method.
-Chapter 9: Identical Particles. The symmetrization postulate. Bosons and
fermions: spin and statistics. Quantum statistics. Pauli's exclusion principle.
Applications.
-M. Le Bellac, Quantum Physics, Cambridge University Press, 2006
-E. S. Abers, Quantum Mechanics, Pearson 2004
-R. Shankar, Principles of Quantum Mechanics, Plenum Press, 1994
-C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics, vols 1 y 2, John Wiley, 1977
-J. J. Sakurai. Modern, Quantum Mechanics, Addison-Wesley 1994.
There are many courses available on the internet of quantum mechanics with an
similar approach to ours and with a similar level. Some of them are:
http://www.courses.physics.helsinki.fi/teor/qme/kvanttiI_notes2014.pdf
(Universidad de Helsinki, Finlandia)
http://amarketplaceofideas.com/wp-content/uploads/2014/06/chap101.pdf
(Universidad de Oslo, Noruega)
http://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/
(MIT, Cambridge, USA)
COMPETENCES:
BASIC AND GENERAL
CB1 - That students have demonstrated to possess and understand knowledge in an area of study that starts from the base of general secondary education, and is usually found at a level that, although supported by advanced textbooks, also includes some aspects that imply knowledge coming from the vanguard of their field of study.
CB2 - That students know how to apply their knowledge to their work or vocation in a professional manner and possess the skills that are usually demonstrated through the elaboration and defense of arguments and the resolution of problems within their area of study.
CB3 - That students have the ability to gather and interpret relevant data (usually within their area of study) to make judgments that include a reflection on relevant issues of social, scientific or ethical nature.
CG1 - Possess and understand the most important concepts, methods and results of the different branches of Physics, with a historical perspective of their development.
CG2 - Have the ability to gather and interpret data, information and relevant results, obtain conclusions and issue reasoned reports on scientific, technological or other issues that require the use of knowledge of Physics.
CG3 - Apply both the theoretical and practical knowledge acquired as well as the capacity for analysis and abstraction in the definition and posing of problems and in the search for their solutions both in academic and professional contexts.
TRANSVERSAL and SPECIFIC
CT1 - Acquire analysis and synthesis capacity.
CT2 - Have the capacity for organization and planning.
CE1 - Have a good understanding of the most important physical theories, locating in their logical and mathematical structure, their experimental support and the physical phenomenon that can be described through them.
CE2 - Be able to clearly handle orders of magnitude and make appropriate estimates in order to develop a clear perception of situations that, although physically different, show some analogy, allowing the use of known solutions to new problems.
CE5 - Be able to perform the essentials of a process or situation and establish a working model of it, as well as perform the required approaches in order to reduce the problem to a manageable level. He will demonstrate critical thinking to build physical models.
CE6 - Understand and master the use of mathematical and numerical methods most commonly used in Physics
A course will be activated in the Moodle platform of the Virtual Campus, which will contain information of interest for the student and different teaching materials.
Lectures and classes of exercises and problems will be made.
The course does not include the realization of a final exam for the first evaluation opportunity. The evaluation system will combine a continuous assesment that will consist in the periodic realization of exercises and problems that the student will deliver. An additional control of greater duration will be performed which evaluates the global competences and that will count up to 75% of the final qualification. For the second evaluation opportunity (July) there will be a conventional final exam.
In cases of fraudulent completion of exercises or tests, the following will apply to the provisions of the "Regulations for evaluating students' academic performance and reviewing grades":
"Article 16. Fraudulent performance of exercises or tests.
The fraudulent performance of any exercise or test required in the evaluation of a subject will imply the qualification of failed in the corresponding call, regardless of the disciplinary process that may be followed against the offending student. It is considered fraudulent, among other things, the realization of plagiarized works or obtained from sources accessible to the public without re-elaboration or reinterpretation and without citations to the authors and the sources ”.
The working time in the classroom in presence of the lecturer, will be of 60 hours, split as follows:
• 32 hours of expositive lectures, in large groups.
• 24 hours of interactive lectures, in reduced groups.
• 4 hours de tutoring for each student.
It is difficult to determine the necessary study time to assimilate the subject, since it depends very much on the dedication and ability of each student. As a general rule, the home work for an average student could be estimated in about 75 hours, excluding the classroom work. Writing exercises or other works in about 15 hours, for a total of 90 hours.
Attendance and participation in class and solving the exercises
proposed is highly recommended.
The tutorials may be face-to-face or telematic and will need an appointment.
Alfonso Vázquez Ramallo
Coordinador/a- Department
- Particle Physics
- Area
- Theoretical Physics
- Phone
- 881813990
- alfonso.ramallo [at] usc.es
- Category
- Professor: University Professor
Xabier Garcia Feal
- Department
- Particle Physics
- Area
- Theoretical Physics
- xabier.garcia.feal [at] usc.es
- Category
- Xunta Post-doctoral Contract
Christoph Adam
- Department
- Particle Physics
- Area
- Theoretical Physics
- Phone
- 881814087
- christoph.adam [at] usc.es
- Category
- Professor: University Lecturer
Juan Santos Suarez
- Department
- Particle Physics
- Area
- Theoretical Physics
- juansantos.suarez [at] usc.es
- Category
- Ministry Pre-doctoral Contract
Marti Berenguer Mimo
- Department
- Particle Physics
- Area
- Theoretical Physics
- marti.berenguer.mimo [at] usc.es
- Category
- Xunta Pre-doctoral Contract
| Tuesday | |||
|---|---|---|---|
| 10:30-11:30 | Grupo /CLE_01 | Spanish | Main Hall |
| 16:00-17:00 | Grupo /CLE_02 | Spanish | Classroom 0 |
| Wednesday | |||
| 10:30-11:30 | Grupo /CLE_01 | Spanish | Main Hall |
| 12:30-14:00 | Grupo /CLE_01 | Spanish | Main Hall |
| 16:00-17:00 | Grupo /CLE_02 | Spanish | Classroom 0 |
| 18:00-19:30 | Grupo /CLE_02 | Spanish | Classroom 0 |
| Thursday | |||
| 10:30-11:30 | Grupo /CLE_01 | Spanish | Main Hall |
| 16:00-17:00 | Grupo /CLE_02 | Spanish | Classroom 0 |
| Friday | |||
| 10:30-11:30 | Grupo /CLE_01 | Spanish | Main Hall |
| 16:00-17:00 | Grupo /CLE_02 | Spanish | Classroom 0 |
| 05.30.2025 09:00-13:00 | Grupo /CLE_01 | Classroom 0 |
| 05.30.2025 09:00-13:00 | Grupo /CLE_01 | Classroom 130 |
| 05.30.2025 09:00-13:00 | Grupo /CLE_01 | Classroom 6 |
| 05.30.2025 09:00-13:00 | Grupo /CLE_01 | Classroom 830 |
| 06.26.2025 09:00-13:00 | Grupo /CLE_01 | Classroom 0 |
| 06.26.2025 09:00-13:00 | Grupo /CLE_01 | Classroom 6 |
| 06.26.2025 09:00-13:00 | Grupo /CLE_01 | Classroom 830 |