A Fulling–Kuchment theorem for the 1D harmonic oscillator
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Gullemin_A Fulling-Kuchment.pdf
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363.32 KB
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Author(s)
Hezari, Hamid
Guillemin, Victor W.
Date Issued
March 2012
Journal
Inverse Problems
Publisher
IOP Publishing
Citation
Guillemin, Victor, and Hamid Hezari. “A Fulling–Kuchment theorem for the 1D harmonic oscillator.” Inverse Problems 28, no. 4 (April 1, 2012): 045009.
Version
Original manuscript
Abstract
We prove that there exists a pair of non-isospectral 1D semiclassical Schrödinger operators whose spectra agree up to O(h∞). 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.
Description
Original manuscript September 5, 2011
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1088/0266-5611/28/4/045009
