Course guide of Quantum Mechanics (2671142)

It is recommended to have passed the following courses: Física General I y II, Álgebra Lineal y Geometría I y II, Mecánica y Ondas and Física Cuántica.

If AI tools were used during the course, students must use these tools from an ethical and responsible perspective. They should follow the guidelines outlined in the document “Recomendaciones para el uso de la inteligencia artificial en la UGR”, available at the following link: https://ceprud.ugr.es/formacion-tic/inteligencia-artificial/recomendaciones-ia#contenido0

Postulates of quantum mechanics.

Identical particles.

Composition of angular momentum.

Approximate methods for non-stationary situations.

Collision theory.

(According to official validation report)

The student will understand:

• the limits of classical physics;

• the relevance of quantum phenomena at different scales;

• the logical structure of quantum mechanics;

• the usefulness of vector spaces and complex numbers in physics;

• the importance of symmetries in physics;

• the peculiarities of the microscopic world;

• the role of collisions in describing that world;

• the difference between “physical” questions and those that are not.

The student will be able to:

• handle the mathematical formalism and apply it to problem-solving;

• properly use the language of quantum mechanics;

• confidently work with concepts such as spin, observable, and cross section;

• use symmetries and conservation laws to study physical processes;

• interpret the results of their calculations.

• Chapter 1. Foundations of quantum mechanics
  Postulados. The space of states. Observables as linear operators. Eigenvalues, eigenstates and projectors. Measurement: the probability of outcomes. The density matrix. Composite systems: entanglement. Time evolution in the Schrödinger and Heisenberg pictures. Quantization rules.

• Chapter 2. Continuous spectrum
  Position representation. Momentum representation. Propagator. Probability density and probability current density. The path integral formulation and the classical limit.

• Chapter 3. Identical particles
  Permutation symmetry. Symmetrization postulate: Pauli exclusion principle. Creation and annihilation operators. Harmonic oscillator.

• Chapter 4. Symmetries
  Symmetry in classical and quantum mechanics. Wigner's theorem. Space translations, rotations and time translations. Conservation laws. Discrete symmetries: parity and time reversal. Internal symmetries.

• Chapter 5. Angular Momentum
  Commutation relations of angular momentum. The rotation group. Spin 1/2 system. Angular momentum representations. Spin and orbital angular momentum. Spherical harmonics. Addition of angular momenta. Vector and tensor operators. Wigner-Eckart theorem.

• Chapter 6. Approximation methods: perturbation theory
  Stationary perturbations. Time-dependent perturbations. Interaction picture. Dyson series. Transition probabibility and Fermi's golden rule.

• Chapter 7. Scattering theory
  Scattering in classical and quantum mechanics. The S-matrix. Poles, bounds and resonances. Ecuación de Lippmann-Schwinger. Scattering amplitudes and cross section. Optical theorem. Born series. Plane waves and spherical waves. Partial-wave S-matrix. Time-independent formalism: stationary states.

• Problem-solving workshops: Discussion of proposed exercises.

• 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 and P. Pascual, "Quantum Mechanics I", Springer-Verlag.
• A. Galindo and P. Pascual, "Quantum Mechanics II", Springer-Verlag.
• D. Tong, "Lectures on Topics in Quantum Mechanics", Cambridge University Press.

• J.J. Sakurai, "Advanced Quantum Mechanics", Addison-Wesley.
• R. Omnès, "Understanding Quantum Mechanics", Princeton University Press.
• D. Griffiths, "Introduction to Quantum Mechanics", Cambridge University Press.
• R. Shankar, "Principles of Quantum Mechanics", Springer.
• R.B. Griffiths, "Consistent Quantum Theory", Cambridge University Press.

• High Energy Theory Group of the University of Granada, https://ftae.ugr.es
• CERN, https://www.cern.ch/
• Quantum mechanics demos with 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/

• MD01. Theoretical classes

• 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: multiple-choice quiz (30% of final grade, subject to previous condition.)

Students who are unable to attend the final assessment tests (ordinaria, extraordinaria, or evaluación única final) due to any of the circumstances listed in Artículo 9 in Normativa de evaluación y de calificación de los estudiantes de la Universidad de Granada may request evaluation due to exceptional circumstances, following the procedure indicated in the aforementioned regulation.

• Assessment in the Extraordinary Examination Session will consist of a written exam covering both theoretical knowledge and problem-solving. This exam will account for 100% of the final grade.

In accordance with the UGR Student Assessment and Grading Regulations, a single final assessment is provided for students who cannot comply with the continuous assessment method for any of the reasons listed in Article 8. To opt for the single final assessment, students must request it online within the first two weeks of the course, within the two weeks following enrollment if this occurs later, or later if there is a supervening reason, stating and accrediting the reasons for not being able to follow the continuous assessment system. The student linked to this type of assessment will take a written exam of theory knowledge and problem solving (100% of final grade).

Students with Specific Educational Support Needs (NEAE): In accordance with the recommendations of CRUE and the Secretariado de Inclusión y Diversidad de la UGR, the systems for acquiring and assessing competencies described in this guide will be applied following the principle of design for all, facilitating learning and the demonstration of knowledge according to the needs and functional diversity of students. Both the teaching methodology and the assessment will be adapted for students with NEAE, in accordance with Artículo 11 in Normativa de Evaluación y de Calificación de los estudiantes de la UGR, published in the Boletín Oficial de la UGR no. 112, dated November 9, 2016. Inclusion and diversity at UGR: For students with disabilities or other NEAE, the tutoring system must be adapted to their needs, in accordance with the recommendations of the Unidad de Inclusión de la UGR, and Departments and Faculties must implement appropriate measures to ensure that tutorials take place in accessible locations. Moreover, upon request by teaching staff, support from the competent university unit may be sought when special methodological adaptations are required. Useful information for students with disabilities and/or Specific Educational Support Needs (NEAE): Service and support management: https://ve.ugr.es/servicios/atencion-social/estudiantes-con-discapacidad

Información de interés para estudiantado con discapacidad y/o Necesidades Específicas de Apoyo Educativo (NEAE): Gestión de servicios y apoyos (https://ve.ugr.es/servicios/atencion-social/estudiantes-con-discapacidad).