An Eigenvalue Inequality for Schrodinger Operators with delta- and delta '-interactions Supported on Hypersurfaces

0456927 - ÚJF 2016 RIV CH eng C - Conference Paper (international conference)
Lotoreichik, Vladimir - Rohleder, J.
An Eigenvalue Inequality for Schrodinger Operators with delta- and delta '-interactions Supported on Hypersurfaces.
Operator Theory Advances and Applications. Vol. 247. Basel: Birkhauser Verlag AG, 2015, s. 173-184. ISBN 978-3-319-18181-3. ISSN 0255-0156.
[24th International Workshop on Operator Theory and Its Applications (IWOTA). Bangalore (IN), 16.12.2013-20.12.2013]
Institutional support: RVO:61389005
Keywords : delta- and delta' - interactions on a hypersurface * discrete spectrum * eigenvalue
Subject RIV: BE - Theoretical Physics

We consider self-adjoint Schrodinger operators in L-2(R-d) with a delta-interaction of strength alpha and a delta'-interaction of strength beta, respectively, supported on a hypersurface, where alpha and beta(-1) are bounded, real-valued functions. It is known that the inequality 0 < beta <= 4/alpha implies inequality of the eigenvalues of these two operators below the bottoms of the essential spectra. We show that this eigenvalue inequality is strict whenever beta < 4/alpha on a nonempty, open subset of the hypersurface. Moreover, we point out special geometries of the interaction support, such as broken lines or infinite cones, for which strict inequality of the eigenvalues even holds in the borderline case beta = 4/alpha.
Permanent Link: http://hdl.handle.net/11104/0257392