Related papers: Schr\"{o}dinger operators with multiple Aharonov-B…
We determine the low-energy behaviour of the scattering operator of two-dimensional Schr\"odinger operators with any type of obstructions at 0-energy. We also derive explicit formulas for the wave operators in the absence of p-resonances,…
We study singular Schr\"odinger operators on a finite interval as selfadjoint extensions of a symmetric operator. We give sufficient conditions for the symmetric operator to be in the $n$-entire class, which was defined in our previous…
In this paper, we study the scattering theory of a class of continuum Schr\"{o}dinger operators with random sparse potentials. The existence and completeness of wave operators are proven by establishing the uniform boundedness of modified…
We consider the Schr\"odinger operator with a periodic potential on quasi-1D models of armchair single-wall nanotubes. The spectrum of this operator consists of an absolutely continuous part (intervals separated by gaps) plus an infinite…
We study the Schr\"odinger operators ${H}_{\lambda\mu}(K)$ with $K\in\mathbb{T}^2$ being the fixed quasimomentum of a pair of particles, associated with a system of two arbitrary particles on a two-dimensional lattice $\mathbb{Z}^2$ with…
We study the Schr\"odinger operator on $L_2(\mathbb R^3)$ with periodic variable metric, and periodic electric and magnetic fields. It is assumed that the operator is reflection symmetric and the (appropriately defined) flux of the magnetic…
In this report we present preliminary results about the tunneling problem for a magnetic Schr\"odinger operator. As a motivation we consider the 3-D time-dependent Schr\"odinger operator $H(t)=-h^2\Delta+V+E(t)\cdot x$ where $V$ is a radial…
This work presents a study on the nonrelativistic quantum motion of a charged particle in a rotating frame, considering the Aharonov-Bohm effect and a uniform magnetic field. We derive the equation of motion and the corresponding radial…
We consider the spectral problem for the two-dimensional Schr\"odinger operator for a charged particle in strong uniform magnetic and periodic electric fields. The related classical problem is analyzed first by means of the…
We investigate a two-dimensional Schr\"odinger operator, $-h^2 \Delta +iV(x)$, with a purely complex potential $iV(x)$. A rigorous definition of this non-selfadjoint operator is provided for bounded and unbounded domains with common…
We provide a simple sufficient condition in an abstract framework to deduce the existence and completeness of wave operators (resp. modified wave operators) on Sobolev spaces from the existence and completeness of the usual wave operators…
A principle is proposed according to which the dynamics of a quantum particle in a one-dimensional configuration space (OCS) is determined by a variational problem for two functionals: one is based on the mean value of the Hamilton…
We consider two-dimensional Schr\"odinger operators in bounded domains. We analyze relations between nodal domains of eigenfunctions, spectral minimal partitions and spectral properties of the corresponding operator. The main results…
We study Schr\"{o}dinger operator $H=-\Delta+V(x)$ in dimension two, $V(x)$ being a limit-periodic potential. We prove that the spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at every point of this…
This paper addresses the scattering of a beam of charged particles by an infinitely long magnetic string in the context of the hydrodynamical approach to quantum mechanics. The scattering is qualitatively analyzed by two approaches. In the…
We study various spectral theoretic aspects of non-self-adjoint operators. Specifically, we consider a class of factorable non-self-adjoint perturbations of a given unperturbed non-self-adjoint operator and provide an in-depth study of a…
Following the approach of our previous paper we continue to study the asymptotic solution of periodic Schr\"{o}dinger operators. Using the eigenvalues obtained earlier the corresponding asymptotic wave functions are derived. This gives…
We continue the analysis started in [Noris,Terracini,Indiana Univ Math J,2010] and [Bonnaillie-No\"el,Noris,Nys,Terracini,Analysis & PDE,2014], concerning the behavior of the eigenvalues of a magnetic Schr\"odinger operator of Aharonov-Bohm…
Quasi-periodic Schr\"odinger-type operators naturally arise in solid state physics, describing the influence of an external magnetic field on the electrons of a crystal. In the late 1970s, numerical studies for the most prominent model, the…
The Hamiltonian of a system of three quantum mechanical particles moving on the three-dimensional lattice $\Z^3$ and interacting via zero-range attractive potentials is considered. For the two-particle energy operator $h(k),$ with $k\in…