Lectures on physical and mathematical aspects of Gamow states

These lectures are devoted to the description of resonances, i.e. Gamow states, in an amenable mathematical formalism. We shall describe Gamow states in scattering theory (S-matrix formalism), in extensions of the conventional Hilbert space (rigged Hilbert spaces and Gelfand triads), and in the Dirac formulation of quantum mechanics (analytical continuations, continuous linear functionals over analytical test functions). Since we aim at further applications in the domain of nuclear structure and nuclear many-body problems, we shall address the issue in a physical oriented manner, restricting the discussion of mathematical concepts to the needed, unavoidable, background.