## Lower bounds on the width of Stark-Wannier type resonances.(English)Zbl 0851.34078

Summary: We prove that the Schrödinger operator $$- d^2/dx^2+ Fx+ W(x)$$ on $$L^2(\mathbb{R})$$ with $$W$$ bounded and analytic in a strip has no resonances in a region $$\text{Im } E\geq -\exp(- C/F)$$.

### MSC:

 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics

### Keywords:

Schrödinger operator; resonances
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