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Schrödinger operators with potential V(n) = n^-γ cos(2π n^ρ)

Helge Krüger

Let H be the Schrödinger operator with potential V(n) = n^-γ cos(2 π n^ρ), where ρ ∈ (1,2) and γ ∈ (0, 1/2 - ρ-1/2 ). I show that for almost every boundary condition H has pure-point spectrum.

MSC2010: Primary 81Q10; Secondary 47B36
Keywords: Schrödinger Operators, pure point spectrum, decaying potentials

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