On the singular spectrum for adiabatic quasiperiodic Schrödinger operators.
On the spectrum and eigenfunctions of the Schrödinger operator with Aharonov–Bohm magnetic field.
On the spectrum of a discrete non-Hermitian quantum system.
On the spectrum of Robin Laplacian in a planar waveguide
We consider the Laplace operator in a planar waveguide, i.e. an infinite two-dimensional straight strip of constant width, with Robin boundary conditions. We study the essential spectrum of the corresponding Laplacian when the boundary coupling function has a limit at infinity. Furthermore, we derive sufficient conditions for the existence of discrete spectrum.
On Threshold Eigenvalues and Resonances for the Linearized NLS Equation
We prove the instability of threshold resonances and eigenvalues of the linearized NLS operator. We compute the asymptotic approximations of the eigenvalues appearing from the endpoint singularities in terms of the perturbations applied to the original NLS equation. Our method involves such techniques as the Birman-Schwinger principle and the Feshbach map.
On wave functions in quantum mechanics
On wave functions in quantum mechanics. Part 3. A theory of quantum mechanics where wave functions are defined by means of surely fundamental observables
Opérateurs de Schrödinger avec champs magnétiques faibles et constants