A Fulling-Kuchment theorem for the 1D harmonic oscillator
Spectral Theory
2015-05-30 v1 Mathematical Physics
Analysis of PDEs
Classical Analysis and ODEs
math.MP
Abstract
We prove that there exists a pair of "non-isospectral" 1D semiclassical Schr\"odinger operators whose spectra agree modulo h^\infty. In particular, all their semiclassical trace invariants are the same. Our proof is based on an idea of Fulling-Kuchment and Hadamard's variational formula applied to suitable perturbations of the harmonic oscillator. Keywords: Inverse spectral problems, semiclassical Schr\"odinger operators, trace invariants, Hadamard's variational formula, harmonic oscillator, Penrose mushroom, Sturm-Liouville theory.
Cite
@article{arxiv.1109.0967,
title = {A Fulling-Kuchment theorem for the 1D harmonic oscillator},
author = {Victor Guillemin and Hamid Hezari},
journal= {arXiv preprint arXiv:1109.0967},
year = {2015}
}
Comments
3 figures