Eigenvalues of Schrödinger operators with complex surface potentials
Abstract
We consider Schrödinger operators in $\mathbb R^d$ with complex potentials supported on a hyperplane and show that all eigenvalues lie in a disk in the complex plane with radius bounded in terms of the $L^p$ norm of the potential with $d1<p\leq d$. We also prove bounds on sums of powers of eigenvalues.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.09067
 Bibcode:
 2015arXiv151209067F
 Keywords:

 Mathematics  Spectral Theory;
 Mathematical Physics
 EPrint:
 12 pages