The first part of this talk is devoted to quantitative uncertainty rela-
tions for Schrödinger operators. Let Ω = ΛL = (−L, L)d or Ω = Rd , and
H = −∆ + V be a Schrödinger operator on L2(Ω) with a bounded poten-
tial V . If Ω = ΛL we impose Dirichlet, Neumann, or periodic boundary
In the second part of the talk is devoted to spectral theory of random
Schrödinger operators. Following an introduction to the topic, we present
a Wegner estimate for the random breather model.
This is joint work with Ivica Nakić, Matthias Täufer and Ivan Veselić.