Sharp Spectral Transition for Eigenvalues Embedded into the Spectral Bands of Perturbed Periodic Schrödinger Operators

@inproceedings{Ong2018SharpST,
  title={Sharp Spectral Transition for Eigenvalues Embedded into the Spectral Bands of Perturbed Periodic Schrödinger Operators},
  author={Darren Ong},
  year={2018}
}
In this paper, we consider the Schrödinger equation, Hu = −u + (V (x) + V0(x))u = Eu, where V0(x) is 1-periodic and V (x) is a decaying perturbation. By Floquet theory, the spectrum of H0 = −∇2 + V0 is purely absolutely continuous and consists of a union of closed intervals (often referred to as spectral bands). Given any finite set of points {Ej}j=1 in any spectral band of H0 obeying a mild non-resonance condition, we construct smooth functions V (x) = O(1) 1+|x| such that H = H0 + V has… CONTINUE READING
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