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Bloch electrons in an external electric field. (English) Zbl 0725.34097
Schrödinger operators, standard and non-standard, Proc. Conf., Dubna/USSR 1988, 103-129 (1989).
Summary: [For the entire collection see Zbl 0722.00018.]
The operator \(H_ 0=H-\epsilon x_ 0\), H being the Schrödinger operator with a periodic potential, is considered. Analytical properties and asymptotic behaviour of the reflectance at \(\epsilon\to 0\) are studied. The relation between resonance asymptotics and quantization conditions characterizing Stark-Wannier ladders is discussed. The connection of “non-eigen” projectors corresponding to resonance states with spectral projectors of the operator \(H_ 0\) is revealed.

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