Stark-Wannier Hamiltonians with pure point spectrum. (English) Zbl 0883.47007

Demuth, Michael (ed.) et al., Differential equations, asymptotic analysis, and mathematical physics. Papers associated with the international conference on partial differential equations, Potsdam, Germany, June 29–July 2, 1996. Akademie Verlag: Akademie Verlag. Math. Res. 100, 10-25 (1997).
Summary: We show that the Kronig-Penney model with a comb of \(\delta'\) interactions plus a homogeneous electric field of strength \(f\) has pure point spectrum for some non “resonant” values of \(f\) and strong enough \(\delta'\).
For the entire collection see [Zbl 0864.00061].


47A55 Perturbation theory of linear operators
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
35P05 General topics in linear spectral theory for PDEs