Course: 2023/2024

Mathematical foundations of quantum mechanics

(18338)

Skills and learning outcomes

Description of contents: programme

On the many pictures of Quantum Mechanics: Schrödinger, Heisenberg and Dirac. An introduction to the theory of Hilbert spaces.
Von Neumann's picture of Quantum Mechanics. The theory of operators, observables and the spectral theorem.
Perturbation theory: stationary and time-dependent perturbation theory, adiabatic theorem, semiclassical approximation, scattering theory.
Weyl's picture of Quantum Mechanics. Weyl's quantization. Coherent states and quantum optics: Wigner's transform and quantum tomography.
Feynman's picture of Quantum Mechanics. The double slit experiment. Feynman's path integral and Dirac's Lagrangian description of Quantum Mechanics.
From particles to fields.
The measurement problem in Quantum Mechanics. Measurement and reversibility. Quantum cloning. Quantum Zeno effect. The nature of quantum states.
EPR. Bell inequalities. Quantum non-locality

Learning activities and methodology

AF1. THEORETICAL-PRACTICAL CLASSES. Knowledge and concepts students mustacquire. Receive course notes and will have basic reference texts.Students partake in exercises to resolve practical problems
AF2. TUTORING SESSIONS. Individualized attendance (individual tutoring) or in-group (group tutoring) for students with a teacher.Subjects with 6 credits have 4 hours of tutoring/ 100% on- site attendance.
AF3. STUDENT INDIVIDUAL WORK OR GROUP WORK.Subjects with 6 credits have 98 hours/0% on-site.
AF8. WORKSHOPS AND LABORATORY SESSIONS. Subjects with 3 credits have 4 hours with 100% on-site instruction. Subjects with 6 credits have 8 hours/100% on-site instruction.
AF9. FINAL EXAM. Global assessment of knowledge, skills and capacities acquired throughout the course. It entails 4 hours/100% on-site
AF8. WORKSHOPS AND LABORATORY SESSIONS. Subjects with 3 credits have 4 hours with 100% on-site instruction. Subjects with 6 credits have 8 hours/100% on-site instruction.
MD1. THEORY CLASS. Classroom presentations by the teacher with IT and audiovisual support in which the subject`s main concepts are developed, while providing material and bibliography to complement student learning
MD2. PRACTICAL CLASS. Resolution of practical cases and problem, posed by the teacher, and carried out individually or in a group
MD3. TUTORING SESSIONS. Individualized attendance (individual tutoring sessions) or in-group (group tutoring sessions) for students with teacher as tutor. Subjects with 6 credits have 4 hours of tutoring/100% on-site.
MD6. LABORATORY PRACTICAL SESSIONS. Applied/experimental learning/teaching in workshops and laboratories under the tutor's supervision.

Assessment System

Basic Bibliography

- A. Galindo, P. Pascual. Quantum Mechanics I. Springer Verlag. 1990
- G. Auletta, M. Fortunato, G. Parisi. Quantum Mechanics. Cambridge Univ. Press. 2009
- G. Esposito, G. Marmo, G. Sudarshan. From Classical to Quantum Mechanics. Cambridge Univ. Press. 2004
- J. Cariñena, A. Ibort, G. Marmo, G. Morandi. Geometry from dynamics: classical and quantum. Springer-Verlag. 2014
- R. Feynman, A. Hibbs. Quantum Mechanics and Path Integrals. Mac-Gray Hill Publish. Co.. 1965

The course syllabus may change due academic events or other reasons.