Some inverse spectral results for semi-classical Schr\"odinger operators
Spectral Theory
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
We consider a semi-classical Schr\"odinger operator, -h^2\Delta + V(x). Assuming that the potential admits a unique global minimum and that the eigenvalues of the Hessian are linearly independent over the rationals, we show that the low-lying eigenvalues of the operator determine the Taylor series of the potential at the minimum.
Cite
@article{arxiv.math/0509290,
title = {Some inverse spectral results for semi-classical Schr\"odinger operators},
author = {V. Guillemin and A. Uribe},
journal= {arXiv preprint arXiv:math/0509290},
year = {2007}
}
Comments
13 pages