Course guide of Quantum Mechanics (2671142)
Grado (bachelor's degree)
Branch
Module
Subject
Year of study
Semester
ECTS Credits
Course type
Teaching staff
Theory
- Manuel Masip Mellado. Grupo: A
- Mikael Rodríguez Chala. Grupo: B
Practice
- Juan Carlos Criado Álamo Grupo: 2
- Manuel Masip Mellado Grupo: 1
- Mikael Rodríguez Chala Grupos: 3 y 4
Timetable for tutorials
Manuel Masip Mellado
Ver email- Monday de 15:00 a 17:00 (Despacho 3)
- Wednesday de 15:00 a 17:00 (Despacho 3)
- Friday de 15:00 a 17:00 (Despacho 3)
Mikael Rodríguez Chala
Ver email- Monday de 15:00 a 17:00 (Despacho 3 Módulo A)
Juan Carlos Criado Álamo
Ver emailPrerequisites of recommendations
It is recommended to have passed the following courses: Física, Métodos Matemáticos, Álgebra Lineal y Geometría, Matemáticas, Mecánica y Ondas and Física Cuántica.
Brief description of content (According to official validation report)
Postulados de la mecánica cuántica.
Partículas idénticas.
Composición de momentos angulares.
Métodos aproximados para situaciones no estacionarias.
Teoría de colisiones.
General and specific competences
General competences
- CG01. Skills for analysis and synthesis
- CG02. Organisational and planification skills
- CG03. Oral and written communication
- CG06. Problem solving skills
- CG07. Team work
- CG08. Critical thinking
- CG09. Autonomous learning skills
- CG10. Creativity
Specific competences
- CE01. Knowing and understanding the phenomena of the most important physical theories
- CE02. Estimating the order of magnitud in order to interpret various phenomena
- CE05. Modelling complex phenomena, translating a physical problem into mathematical language
- CE07. Transmitting knowledge clearly, both in academic as in non-academic contexts
- CE09. Applying mathematical knowlegde in the general context of Physics
Objectives (Expressed as expected learning outcomes)
(According to official validation report)
El alumno comprenderá:
- los límites de la física clásica;
- la relevancia de los fenómenos cuánticos a distintas escalas;
- la estructura lógica de la mecánica cuántica;
- la utilidad de los espacios vectoriales y los números complejos en física;
- la importancia de las simetrías en física;
- las peculiaridades del mundo microscópico;
- el papel de las colisiones en la descripción de ese mundo;
- la diferencia entre cuestiones “físicas” y cuestiones que no lo son.
El alumno estará capacitado para:
- manejar el formalismo matemático y aplicarlo a la resolución de problemas;
- usar con propiedad el lenguaje de la mecánica cuántica;
- manejar con seguridad conceptos como espín, observable o sección eficaz;
- usar simetrías y leyes de conservación para estudiar procesos físicos;
- interpretar los resultados de sus cálculos.
Detailed syllabus
Theory
- Chapter 1. Fundamentals of quantum mechanics
Stern-Gerlach experiment. Pure states. Observables. Eigenvalues, eigenstates and projectors. Measurement and probability. Density matrix. Composite systems. Continuous spectrum: Dirac formalism.
- Chapter 2. Symmetries
Symmetry in quantum mechanics. Wigner's theorem. Symmetry groups and their representations. Observables as generators of continous symmetries.
- Chapter 3. Time translations
Time evolution. Hamiltonian. Schrödinger and Heisenberg pictures. Conservation laws.
- Chapter 4. Space translations
Position operator. Momentum. Wave function. Classic limit. Propagator. Path integral.
- Chapter 5. Rotations
Rotation group. Angular momentum. Irreducible representations. Orbital angular momentum. Spin. Addition of angular momentum. Tensor operators.
- Chapter 6. Internal and discrete symmetries
Parity. Time reversal. Isospin.
- Chapter 7. Identical particles
Permutation symmetry. Spin-statistics theorem. Systems of identical particles. Creation and annihilation operators.
- Chapter 8. Time-dependent perturbation theory
Interaction picture. Dyson series. Transition probability. Transition to the continuum.
- Chapter 9. Scattering theory.
Asymptotic behaviour. S matrix. Scattering amplitudes and cross section. Optical theorem. Born series. Stationary methods: Green's operators, scattering states, Lippman-Schwinger equation. Partial waves.
Practice
- Problem-solving workshops:Discussion of proposed exercises.
- Oral presentations by students, subject to time constraints.
Bibliography
Basic reading list
- S. Weinberg, Lectures in Quantum Mechanics, Cambridge University Press.
- J.J. Sakurai, Modern Quantum Mechanics, Addison-Wesley.
- J.R. Taylor, Scattering Theory, J. Wiley.
- A. Galindo y P. Pascual, Mecánica Cuántica, Eudema Universidad.
Complementary reading
- A. Messiah, Mecánica Cuántica, Tecnos.
- D. Bohm, Quantum Theory, Dover.
- F.J. Yndurain, Mecánica Cuántica, Alianza Editorial Textos.
- L.E. Ballentine, Quantum Mechanics. A Modern Development, World Scientific.
- R.P. Feynman, R. Leighton, M. Sands, The Feynman lectures on physics- Vol. III. Addison- Wesley.
- P. Dirac, The Principles of Quantum Mechanics, Oxford University Press.
Recommended links
- Grupo de física de partículas de la UGR, https://ftae.ugr.es
- CERN, https://www.cern.ch/
- Particle Data Group, https://pdg.web.cern.ch/pdg/
- Demostraciones de Mecánica Cuántica con Mathematica, https://demonstrations.wolfram.com/topic.html?topic=Quantum+Mechanics
- MIT OpenCourseWare, Quantum Physics II, https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/
- MIT OpenCourseWare, Quantum Physics III, https://ocw.mit.edu/courses/physics/8-06-quantum-physics-iii-spring-2018/
Teaching methods
- MD01. Theoretical classes
Assessment methods (Instruments, criteria and percentages)
Ordinary assessment session
- Final exam of theory knowledge and/or problem solving (70% of final grade). Passing the exam is strictly necessary to pass the course.
- Continuous assessment: participation in class, problem solving, multiple-choice quiz, written work, presentations (30% of final grade, subject to previous condition.)
Extraordinary assessment session
- Exam of theory knowledge and/or problem solving (100% of final grade).
Single final assessment
The student who, following the terms and deadlines envisaged in the UGR regulations, makes use of this form of assessment, will take a written exam of knowledge and problem solving in order to pass the course.