Mathematics

1. Mathematical foundations of quantum mechanics. ¿ Wave function space. Scalar (inner) product. Linear operators. ¿ Discrete and continuous basis. Basis of the space. ¿ Orthogonality, orthonormality and completeness. ¿ State Space. Dirac notation. ¿ Hermitian operators. Representation of operators on a space basis. Operators and physical observables ¿ Eigenvalues and eigenvectors. ¿ Matrix formulation of Quantum Mechanics. ¿ Tensor product of state spaces. 2. Postulates of quantum mechanics. ¿ Postulates of Quantum Mechanics. ¿ Space of states. ¿ Time evolution of quantum systems. ¿ Spectral decomposition. ¿ Quantum measurement and uncertainty. 3. Quantum harmonic oscillator. ¿ Introduction. ¿ Quantum harmonic oscillator. ¿ Coherent states. ¿ Squeezed states. 4. Theory of Angular Momentum. ¿ Introduction. ¿ General theory of angular momentum. ¿ Orbital angular momentum ¿ Spin angular momentum. Stern-Gerlach experiment ¿ Spin-orbit interaction ¿ Zeeman effect 6. Introduction to quantum computing. ¿ Pure and mixed states. ¿ Qubits. ¿ Bell states. ¿ Quantum entanglement.

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.