Understand the formalism of quantum mechanics. To know how to quantize a classical system. Understand the behavior of systems of identical particles. Master the use of principles of symmetry in Quantum Mechanics. To know how to calculate cross sections.

Generic skills: Competence in oral and written communication; Competence to solve problems; Competence in independent learning; Adaptability to new situations; Competence to investigate; Group work in competence; Competence in critical thinking; Competence to communicate with people who are not experts in the field;

Systems of identical particles: the principle of indistinguishability. Exchange Operators. Exchange degeneracy and the postulate of symmetrization.

Symmetries in Quantum Mechanics: symmetry transformations and operators that represent symmetry transformations. Symmetry groups. Groups of continuous transformations: generators and the maximum set of operators that commute. The decomposition of the Hilbert space in invariant subspaces. Operators for finite transformations and their relationship with generators. Lie algebras. Casimir operators. Discrete symmetry transformations. Scalar, pseudoscalar, vector and pseudo vector operators and selection rules. The temporal inversion. The Kramer degeneration of Kramer.

Theory of Collisions: cross sections and scattering amplitudes. Dispersion by a central potential, phase shifts partial wave decomposition. Unitarity. Potentials of finite range.

Quantum Mechanics I