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arXiv · 1109.0967

A Fulling-Kuchment theorem for the 1D harmonic oscillator

Victor Guillemin·Hamid Hezari
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Abstract

We prove that there exists a pair of "non-isospectral" 1D semiclassical Schrödinger 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 Schrödinger operators, trace invariants, Hadamard's variational formula, harmonic oscillator, Penrose mushroom, Sturm-Liouville theory.

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BibTeXRIS

Victor Guillemin, Hamid Hezari. 2011-09-05. A Fulling-Kuchment theorem for the 1D harmonic oscillator. https://doi.org/10.1088/0266-5611%2F28%2F4%2F045009

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