Mathematics

Contents common to all courses: - - Postulates of Quantum Mechanics. - - Quantum state. Space of quantum states. - - Physical magnitudes and operators. Eigenvalues and Eigenstates. - - Quantum measurement. - - Quantum harmonic oscillator and coherent states. - - Quantum entanglement. Contents specific to each course: Matrix quantum mechanics: - - Finite vector spaces. Bras and kets. Inner product. Basis of the space. Orthogonality, orthonormality and completeness. Decompositions. - - Operators. Representations of operators on a space basis. Eigenvalues and eigenvectors. Adjoint operator. Hermitian, unitary and normal operator. Projector operators, Commutators. Tensor products - - Postulates of quantum mechanics. Space of states. Operators and physical observables. Quantum measurement and uncertainties. Evolution of the quantum state. - - Pure and mixed states. Examples of 2D quantum 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.