Buslaev, V. S.; Dmitrieva, L. A. 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. Cited in 3 Documents 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; Analytical properties; asymptotic behaviour of the reflectance; resonance asymptotics; Stark-Wannier ladders Citations:Zbl 0722.00018 PDFBibTeX XML