Course guide of Quantum Mechanics (2671142)

Curso 2022/2023
Approval date: 20/06/2022

Grado (bachelor's degree)

Bachelor'S Degree in Physics

Branch

Sciences

Module

Fundamentos Cuánticos

Subject

Mecánica Cuántica

Year of study

4

Semester

1

ECTS Credits

6

Course type

Compulsory course

Teaching staff

Theory

  • Manuel María Pérez-Victoria Moreno de Barreda. Grupo: A
  • Mikael Rodríguez Chala. Grupo: B

Practice

  • Francisco Javier Nicolás Arnaldos Grupo: 2
  • Manuel María Pérez-Victoria Moreno de Barreda Grupo: 1
  • Mikael Rodríguez Chala Grupos: 3 y 4

Timetable for tutorials

Manuel María Pérez-Victoria Moreno de Barreda

Email
  • Tuesday de 10:00 a 12:00 (Despacho 20)
  • Wednesday de 10:00 a 12:00 (Despacho 20)
  • Thursday de 10:00 a 12:00 (Despacho 20)

Mikael Rodríguez Chala

Email
  • Wednesday de 15:00 a 17:00 (Despacho 3 Módulo A)

Francisco Javier Nicolás Arnaldos

Email
  • Tuesday de 10:00 a 11:00 (Despacho 29)
  • Wednesday de 10:00 a 10:30 (Despacho 29)

Prerequisites 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

  • J.J. Sakurai, Modern Quantum Mechanics, Addison-Wesley
  • J.R. Taylor, Scattering Theory, J. Wiley.
  • A. Galindo y P. Pascual, Mecánica Cuántica, Eudema Universidad.
  • P. Dirac, The Principles of Quantum Mechanics, Oxford University Press.

Complementary reading

  • S. Weinberg, Lectures in Quantum Mechanics, Cambridge University Press.
  • 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.

Recommended links

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.