Ultimate Sidebar
Browsing Category

A Fulling–Kuchment theorem for the 1D harmonic oscillator;

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