ABSTRACT
We investigate the Schrödinger operators in
with the short-range potentials
which are localized around a smooth closed curve γ. The operators
can be viewed as an approximation of the heuristic Hamiltonian
, where
is Dirac's δ-function supported on γ and
is its normal derivative on γ. Assuming that the operator
has only discrete spectrum, we analyse the asymptotic behaviour of eigenvalues and eigenfunctions of
. The transmission conditions on γ for the eigenfunctions
,
which arise in the limit as
reveal a nontrivial connection between spectral properties of
and the geometry of γ.
2000 Mathematics Subject Classifications:
Disclosure statement
No potential conflict of interest was reported by the author(s).