Non-accretive Schr\"odinger operators and exponential decay of their eigenfunctions
Spectral Theory
2018-11-26 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We consider non-self-adjoint electromagnetic Schr\"odinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic potential, we introduce a Dirichlet realisation as a closed densely defined operator with non-empty resolvent set and show that the eigenfunctions corresponding to discrete eigenvalues satisfy an Agmon-type exponential decay.
Keywords
Cite
@article{arxiv.1605.02437,
title = {Non-accretive Schr\"odinger operators and exponential decay of their eigenfunctions},
author = {David Krejcirik and Nicolas Raymond and Julien Royer and Petr Siegl},
journal= {arXiv preprint arXiv:1605.02437},
year = {2018}
}