01018nas a2200121   4500008004100000245007900041210007000120260001000190520058700200100002900787700002900816856005100845       2015                        en  d00aSchödinger operators on half-line with shrinking potentials at the origin0 aSchödinger operators on halfline with shrinking potentials at th  bSISSA3 aWe discuss the general model of a Schrödinger quantum particle
constrained on a straight half-line with given self-adjoint boundary condition at the origin and an interaction potential supported around the origin. We study the limit when the range of the potential scales to zero and its magnitude blows up. We show that in the limit the dynamics is generated by a self-adjoint negative Laplacian on the half-line, with a possible preservation or modification of the boundary condition at the origin, depending on the magnitude of the scaling and of the strength of the potential.1 aDell'Antonio, Gianfausto1 aMichelangeli, Alessandro  uhttp://urania.sissa.it/xmlui/handle/1963/34439