Related papers: Schr\"{o}dinger operators with multiple Aharonov-B…
We consider a Schroedinger operator on the axis with a bipartite potential consisting of two compactly supported complex-valued functions, whose supports are separated by a large distance. We show that this operator possesses a sequence of…
We propose a simple situation in which the magnetic Aharonov-Bohm potential influences the values of the deficiency indices of the initial Schr\"odinger operator, so determining whether the particle interacts with the solenoid or not. Even…
We consider two-dimensional Schr\"odinger operators $H$ with Aharonov-Bohm magnetic field and an additional electric potential. We obtain an explicit leading term of the asymptotic expansion of the unitary group $e^{-i t H}$ for…
This paper is on magnetic Schrodinger operators in two dimensional domains with corners. Semiclassical formulas are obtained for the sum and number of eigenvalues. The obtained results extend former formulas for smooth domains in \cite{Fr,…
We investigate the multidimensional Schrodinger operator L(q) with complex-valued periodic, with respect to a lattice, potential q when the Fourier coefficients of q with respect to the orthogonal system {exp(i(a,x))}, where a changes in…
We study the theory of scattering for a Schr"odinger equation in an external time dependent magnetic field in the Coulomb gauge, in space dimension 3. The magnetic vector potential is assumed to satisfy decay properties in time that are…
We consider 2-dimensional Schroedinger operator with the non-degenerating magnetic field in the domain with the boundary and under certain non-degeneracy assumptions we derive spectral asymptotics with the remainder estimate better than…
We consider a simple modification of the 1D-Laplacian where non-mixed interface conditions occur at the boundaries of a finite interval. It has recently been shown that Schr\"odinger operators having this form allow a new approach to the…
Schr\"odinger operators often display singularities at the origin, the Coulomb problem in atomic physics or the various matter coupling terms in the Friedmann-Robertson-Walker problem being prominent examples. For various applications it…
We show that in the absence of a magnetic field the spectrum of the magnetic Schr\"odinger operator in an annulus depends on the cosine of the flux associated with the magnetic potential. This result follows from an analysis of a…
This survey is a short version of a chapter written by the first two authors in the book [A. Henrot, editor. Shape optimization and spectral theory. Berlin: De Gruyter, 2017] (where more details and references are given) but we have decided…
For any positive real number $s$, we study the scattering theory in a unified way for the fractional Schr\"{o}dinger operator $H=H_0+V$, where $H_0=(-\Delta)^\frac s2$ and the real-valued potential $V$ satisfies short range condition. We…
This paper addresses the single-valued requirement for quantum wave functions when they are analytically continued in the spatial coordinates. This is particularly relevant for de Broglie-Bohm, hydrodynamic, or stochastic models of quantum…
In this work, we study the scattering of a spinless charged particle constrained to move on a curved surface in the presence of the Aharonov-Bohm potential. We begin with the equations of motion for the surface and transverse dynamics…
The discrete one-dimensional Schr\"odinger operator is studied in the finite interval of length $N=2 M$ with the Dirichlet boundary conditions and an arbitrary potential even with respect to the spacial reflections. It is shown, that the…
We consider 2-dimensional Schr\"odinger operator with the non-degenerating magnetic field and we discuss spectral asymptotics with the remainder estimate $o(\mu^{-1}h^{-1})$ or better. We also consider 3-dimensional Schr\"odinger operator…
We consider the hamiltonian operator associated with planar sec- tions of infinitely long cylindrical solenoids and with a homogeneous magnetic field in their interior. First, in the Sobolev space $\mathcal H^2$, we characterize all…
We study the Schr\"odinger operator with a potential given by the sum of the potentials for harmonic oscillator and imaginary cubic oscillator and we focus on its pseudospectral properties. A summary of known results about the operator and…
We study the spectrum of a one-dimensional Schroedinger operator perturbed by a fast oscillating potential. The oscillation period is a small parameter. The essential spectrum is found in an explicit form. The existence and multiplicity of…
We consider an electrically charged particle on the Euclidean plane subjected to a perpendicular magnetic field which depends only on one of the two Cartesian co-ordinates. For such a ``unidirectionally constant'' magnetic field (UMF),…