Some problems of numerical and functional analysis in nuclear physics

An essential feature of nuclear physics is that the number of degrees of freedom to be described is at the same time too large to give rise to problems exactly soluble in practice and too small to warrant entire recourse to statistical mechanics. Nuclear physics experiments show clearly in fact that the behaviour of nuclei is sometimes reduced to the variation of one (or several) degree(s) of freedom known as collective, whereas in other cases no order parameter seems to be identifiable. Since all situations between these two extremes are possible, and actually arise, an essential problem in this branch of physics is the construction of a mathematical method to reduce systematically the number of degrees of freedom. This problem is illustrated here by an analysis of Schroedinger equation, then of the Hartree-Fock equation and finally of the generator-coordinate method for the collision theory