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Stark Wannier ladders. (English) Zbl 0743.35053

Summary: We study the Schrödinger equation for an electron in a one dimensional crystal submitted to a constant electric field. We prove the existence of ladders of resonances, the imaginary part of which is exponentially small with the field.

MSC:

35Q40 PDEs in connection with quantum mechanics
35P05 General topics in linear spectral theory for PDEs
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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