TY - RPRT
T1 - SchÃ¶dinger operators on half-line with shrinking potentials at the origin
Y1 - 2015
A1 - Gianfausto Dell'Antonio
A1 - Alessandro Michelangeli
AB - We discuss the general model of a SchrÃ¶dinger 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.
PB - SISSA
UR - http://urania.sissa.it/xmlui/handle/1963/34439
U1 - 34566
ER -