In this talk we discuss a family of Schrödinger operators with so-called oblique transmission conditions. The considered transmission conditions are similar to those associated with Schrödinger operators with delta'-potentials, but instead of the normal derivative, the Wirtinger derivative on a sufficiently smooth closed curve in R2 is prescribed. Using boundary triplet techniques, self-adjointness as well as spectral properties are studied. In particular, it is shown for attractive interactions that the discrete spectrum for this class of Schrödinger operators is countable and unbounded from below.
Finally, we show that these operators occur naturally as non-relativistic limits of Dirac operators with electrostatic and Lorentz scalar delta-potentials when the limit c to infinity is carried out in a suitable way. This generalises a well-known result about the non-relativistic limit of one dimensional Dirac operators with delta'-interactions.
This is joint work with Jussi Behrndt and Markus Holzmann.