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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F15%3A00456927" target="_blank" >RIV/61389005:_____/15:00456927 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
An Eigenvalue Inequality for Schrodinger Operators with delta- and delta '-interactions Supported on Hypersurfaces
Original language description
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 isknown 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.
Czech name
—
Czech description
—

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)