Momentum approach to the 1/r2 potential as a toy model of the Wilsonian renormalization

Abstract

The Bessel operator, that is, the Schrödinger operator on the half-line with a potential proportional to 1/x2, is analyzed in the momentum representation. Many features of this analysis are parallel to the approach according to Wilson on quantum field theory: one needs to impose a cutoff, add counterterms, and study the renormalization group flow with its fixed points and limit cycles.