Application of renormalization group techniques to the solution of integrals and Schrodinger eigenvalue equations

The renormalization group (RG) consists of a set of concepts and methods which can be used to analyze phenomena in many different fields of mathematics and physics, ranging from probability theory and statistical mechanics, to nonequilibrium phenomena. These RG techniques are particularly useful in order to study fluctuations on top of a mean-field like solution. In the last two decades the development of the so-called functional renormalization group (FRG) method has provided a mathematically elegant and yet simple way of expressing Wilson’s idea of successive mode elimination in terms of a formally exact functional differential equation for the effective action (also known as the Ginzburg-Landau free energy in condensed matter contexts). The aim of the Thesis is to apply FRG tools to two problems: the study of non-trivial one variable and multivariable integrals, and the determination of the energy spectrum of the Schrödinger equation.