## Resonances for perturbed periodic Schrödinger operator.(English)Zbl 1236.81082

Summary: In the semiclassical regime, we obtain a lower bound for the counting function of resonances corresponding to the perturbed periodic Schrödinger operator $$P(h) = -\Delta + V(x) + W(hx)$$, where $$V$$ is a periodic potential, $$W$$ a decreasing perturbation and $$h$$ a small positive constant.

### MSC:

 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 49S05 Variational principles of physics 35B34 Resonance in context of PDEs 81Q15 Perturbation theories for operators and differential equations in quantum theory
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### References:

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