A Fulling–Kuchment theorem for the 1D harmonic oscillator

Author(s)
Hezari, Hamid; Guillemin, Victor W.
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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
Date issued
2012-03
URI
http://hdl.handle.net/1721.1/80859
Department
Massachusetts Institute of Technology. Department of Mathematics
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
ISSN
0266-5611
1361-6420
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