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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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