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. 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.

• Problem-solving workshops: Discussion of proposed exercises.

• 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".

• 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".

• 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: participation in class, problem solving, multiple-choice quiz, written work, presentations (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.

• Exam of theory knowledge and/or problem solving in order to reach all the learning outcomes (100% of 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