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math.SP2021
Discrete Schrödinger operators with decaying and oscillating potentials
Rupert L. Frank, Simon Larson
We study a family of discrete one-dimensional Schrödinger operators with power-like decaying potentials with rapid oscillations. In particular, for the potential $V(n)=λn^{-α}\cos(…
math-ph2021★ 1 cited
On the spectrum of the Kronig-Penney model in a constant electric field
Rupert L. Frank, Simon Larson
We are interested in the nature of the spectrum of the one-dimensional Schrödinger operator $$ - \frac{d^2}{dx^2}-Fx + \sum_{n \in \mathbb{Z}}g_n δ(x-n) \qquad\text{in } L^2(\mathb…