J. Behrndt, M. Langer and V. Lotoreichik,
Boundary triples for Schrödinger operators with singular interactions on hypersurfaces,
Nanosystems: Phys. Chem. Math. 7 (2016), 290–302
Abstract:
The self-adjoint Schrödinger operator Aδ,α
with a δ-interaction of constant strength α supported on a compact smooth
hypersurface C is viewed as a self-adjoint extension of a natural underlying
symmetric operator S in L2(ℝn).
The aim of this note is to construct a boundary triple for S*
and a self-adjoint parameter Θδ,α in the
boundary space L2(C) such that Aδ,α
corresponds to the boundary condition induced by Θδ,α.
As a consequence the well-developed theory of boundary triples and their Weyl functions
can be applied. This leads, in particular, to a Krein-type resolvent formula and
a description of the spectrum of Aδ,α in terms of the
Weyl function and Θδ,α.