course specifications - Departamento de Física da Universidade de Coimbra

Hilbert space. Postulates of Quantum Mechanics. Time development of a wave packet. Uncertainty relationships of position-momentum and energy-time. Schroedinger and Klein-Gordon wave equations for bosons and Dirac wave equations for fermions.

Bound states: Coulomb potential and the hydrogen atom. The one dimensional harmonic oscillator and creation and annihilation operators. The three dimensional harmonic oscillator in Cartesian Coordinates and spherical coordinates.

Comparison of degeneration in both cases.

Dispersion: Dispersion of a wave packet to a fixed target. S and T Matrices. Phase deviation and its calculation based on the simple potentials.

Symmetries in Quantum Mechanics: symmetry transformations and operators on Hilbert space that represent symmetry transformations. Symmetry groups. Symmetry operators and the states of Hamiltonian. Continuous transformation groups: transformation generators and their relation to the maximal set of operators they commute. The decomposition of the state space into invariant subspaces. Lie Algebra. Casimir operators. Space translations operators, movement through time and rotations. SO(3) and SU(2) matrices groups. J, L, S and P quantum numbers for particle systems. Pauli Matrices. Scale, pseudoscale, vector and pseudo-vector operators and rules of selection. Time inversion.

Quark-antiquark systems and their properties.

Prerequisites

Quantum Mechanics I.

Generic skills to reach

. Competence in oral and written communication;
. Competence to solve problems;
. Competence in autonomous learning;
. Adaptability to new situations;
. Research skills;
. Competence for working in group;
. Critical thinking;
. Competence to communicate with people who are not experts in the field;
(by decreasing order of importance)

Teaching hours per semester