We discuss the general model of a Schrödinger quantum particle constrained on a straight half-line with given selfadjoint 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. © 2016 - IOS Press and the authors. All rights reserved.

Schrodinger operators on half-line with shrinking potentials at the origin

Dell'Antonio, Gianfausto;Michelangeli, Alessandro
2016-01-01

Abstract

We discuss the general model of a Schrödinger quantum particle constrained on a straight half-line with given selfadjoint 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. © 2016 - IOS Press and the authors. All rights reserved.
2016
97
1-2
113
138
Dell'Antonio, Gianfausto; Michelangeli, Alessandro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/32546
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