  We show that there exist pairs of non-isometric potentials for the 1D
semiclassical Schr\"odinger operator whose spectra agree up to $O(h^\infty)$,
yet their corresponding eigenvalues differ no less than exponentially. This
result was conjectured by Guillemen and Hezari in [GH12], where they prove a
very similar result, yet cannot remove the possibility of a subsequence $h_k\to
0$ where the ground state eigenvalues may agree.
