Course guide of Quantum Mechanics (2671142)

Curso 2024/2025
Approval date: 10/06/2024

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 Masip Mellado. Grupo: A
  • Mikael Rodríguez Chala. Grupo: B

Practice

  • Juan Carlos Criado Álamo Grupo: 1
  • José Ignacio Illana Calero Grupo: 2
  • Mikael Rodríguez Chala Grupos: 3 y 4

Timetable for tutorials

Manuel Masip Mellado

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  • 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

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

Juan Carlos Criado Álamo

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  • Monday de 11:00 a 13:00 (Despacho 23)
  • Tuesday de 11:00 a 13:00 (Despacho 23)
  • Wednesday de 11:00 a 13:00 (Despacho 23)

José Ignacio Illana Calero

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  • Monday de 11:00 a 13:00 (Despacho A4 Módulo)
  • Wednesday de 11:00 a 13:00 (Despacho A4 Módulo)
  • Friday de 11:00 a 13:00 (Despacho A4 Módulo)

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

Pure states. Observables. Eigenvalues, eigenstates and projectors. Density matrix. Continuous spectrum.

  • Chapter 2. Composite systems

Systems of identical particles. Pauli exclusion principle. Creation and annihilation operators. Entanglement.

  • Chapter 3. Quantum foundations

Hidden variables, CHSH inequality and GHZ states. Quantum computing. The measurement problem and solutions. Decoherence.

  • Chapter 4. Symmetries

Symmetry in quantum mechanics. Wigner's theorem. Groups and representations. Observables as generators of continous symmetries.

  • Chapter 5. Time and space translations

Hamiltonian. Schrödinger and Heisenberg pictures. Conservation laws. Position operator. Momentum.

  • Chapter 6. Rotations

Group of rotations. Angular momentum. Irreducible representations. Spin-statistics theorem. Addition of angular momentum. Tensor operators.

  • Chapter 7. Internal and discrete symmetries

Parity. Time reversal. Isospin.

  • Chapter 8. Time-dependent perturbation theory

Interaction picture. Dyson series. Transition probability.

  • Chapter 9. Scattering theory.

Asymptotic behaviour. S matrix. Scattering amplitude and cross section. Partial waves. Optical theorem. Lippman-Schwinger equation, Green's operators and Born series.

Practice

  • Problem-solving workshops: Discussion of proposed exercises.

Bibliography

Basic reading list

  • S. Weinberg, "Lectures in Quantum Mechanics".
  • J.J. Sakurai, "Modern Quantum Mechanics".
  • A. Galindo and P. Pascual, "Quantum Mechanics I".
  • A. Galindo and P. Pascual, "Quantum Mechanics II".
  • D. Tong, "Lectures on Topics in Quantum Mechanics".

Complementary reading

  • J.J. Sakurai, "Advanced Quantum Mechanics".
  • R. Omnès, "Understanding Quantum Mechanics".
  • D. Griffiths, "Introduction to Quantum Mechanics".
  • R. Shankar, "Principles of Quantum Mechanics".
  • R.B. Griffiths, "Consistent Quantum Theory".

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.