From a review of the first edition: Beautifully written and well organized... indispensable for
those interested in certain areas of mathematical physics... for the expert and beginner alike …

Schrödinger operators in the twentieth century | Journal of Mathematical Physics | AIP
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∂ tu=(ϵ+ V) u+ δ| u| 2pu(p> 0)(1.1) on Zd×[0,∞), where 0< ϵ, δ≪ 1, is the discrete
Laplacian: ij={1,| i− j| l1= 1, 0, otherwise,(1.2) and V={vj} j∈ Zd, the potential, is a family of …

9.1 Introduction Anderson (1958) published an article where he discussed the behaviour of
electrons in a dirty crystal. This is the quantum mechanical analogue of a random walk in a …

Random Schrödinger operators are models for the quantum mechanical description of
disordered media. The main aim of the analysis of such models is the understanding of the …

In this paper, we study the discrete nonlinear random Schrödinger equation i∂∂ tu=(ε Δ+ V)
u+ δ| u| 2 pu (p∈ N+) on Z d×[0,∞)⁠, where 0< ɛ, δ≪ 1, Δ is the discrete Laplacian, and V …

We prove that at large disorder, with large probability and for a corresponding set of
Diophantine frequencies of large measure, Anderson localization in ℤ d is stable under …

We prove Anderson localization with the mean-field Lyapunov exponent and Poisson
statistics for eigenvalue spacing for the multi-dimensional Anderson model at weak disorder …

Electronic properties of amorphous or non-crystalline disordered solids are often modelled
by one-particle Schrödinger operators with random potentials which are ergodic with respect …

We survey recent results on spectral properties of random Schr\" odinger operators. The
focus is set on the integrated density of states (IDS). First we present a proof of the existence …