Some Schrödinger Operators with Dense Point Spectrum

  title={Some Schr{\"o}dinger Operators with Dense Point Spectrum},
  author={Barry Simon},
Given any sequence {En}n−1 of positive energies and any monotone function g(r) on (0,∞) with g(0) = 1, lim r→∞ g(r) = ∞, we can find a potential V (x) on (−∞,∞) so that {En}n=1 are eigenvalues of − d 2 dx2 + V (x) and |V (x)| ≤ (|x| + 1)−1g(|x|). In [7], Naboko proved the following: Theorem 1. Let {κn}∞n=1 be a sequence of rationally independent positive reals. Let g(r) be a monotone function on [0,∞) with g(0) = 1, lim r→∞ g(r) = ∞. Then there exists a potential V (x) on [0,∞) so that (1) {κ2n… CONTINUE READING
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