A New Class of Schr\"odinger Operators without Positive Eigenvalues
Spectral Theory
2018-10-09 v2 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
Following the proof given by Froese and Herbst in [FH82] with another conjugate operator, we show for a class of real potential that possible eigenfunction of the Schr\"odinger operator has to decay sub-exponentially. We also show that, for a certain class of potential, this bound can not be satisfied which implies the absence of strictly positive eigenvalues for the Schr\"odinger operator.
Cite
@article{arxiv.1711.07381,
title = {A New Class of Schr\"odinger Operators without Positive Eigenvalues},
author = {Alexandre Martin},
journal= {arXiv preprint arXiv:1711.07381},
year = {2018}
}