Related papers: Calogero type bounds in two dimensions
We prove that the number of negative eigenvalues of two-dimensional magnetic Schroedinger operators is bounded from above by the strength of the corresponding electric potential. Such estimates fail in the absence of a magnetic field. We…
We derive weighted versions of the Cwikel-Lieb-Rozenblum inequality for the Schr\"odinger operator in two dimensions with a nontrivial Aharonov-Bohm magnetic field. Our bounds capture the optimal dependence on the flux and we identify a…
A fundamental result of Solomyak says that the number of negative eigenvalues of a Schr\"odinger operator on a two-dimensional domain is bounded from above by a constant times a certain Orlicz norm of the potential. Here we show that in the…
We consider the ground state $\phi_0$ of the Schr\"odinger operator $L=-\Delta+V$ on the bounded convex domain $\Omega\subset\R^n$, satisfying the Dirichlet boundary condition. Assume that $V\in C^1(\Omega)$ and it admits an even function…
We prove a certain upper bound for the number of negative eigenvalues of the Schr\"{o}dinger operator on the plane.
It is shown that for the Calogero-Cohn type upper bounds on the number of bound states of a negative spherically symmetric potential $V(r)$, in each angular momentum state, that is, bounds containing only the integral $\int^\infty_0…
We prove upper and lower bounds for the number of eigenvalues of semi-bounded Schr\"odinger operators in all spatial dimensions. As a corollary, we obtain two-sided estimates for the sum of the negative eigenvalues of atomic Hamiltonians…
Given a Schr\"odinger operator with a real-valued potential on a bounded, convex domain or a bounded interval we prove inequalities between the eigenvalues corresponding to Neumann and Dirichlet boundary conditions, respectively. The…
We show that an electric potential and magnetic field can be uniquely determined by partial boundary measurements of the Neumann-to-Dirichlet map of the associated magnetic Schr\"{o}dinger operator. This improves upon previous results of…
This paper is devoted to the symmetry and symmetry breaking properties of a two-dimensional magnetic Schr{\"o}dinger operator involving an Aharonov-Bohm magnetic vector potential. We investigate the symmetry properties of the optimal…
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 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…
We prove Lieb-Thirring inequalities for Schr\"odinger operators with a homogeneous magnetic field in two and three space dimensions. The inequalities bound sums of eigenvalues by a semi-classical approximation which depends on the strength…
We consider the multidimensional Borg-Levinson theorem of determining both the magnetic field $dA$ and the electric potential $V$, appearing in the Dirichlet realization of the magnetic Schr\"odinger operator $H=(-{\rm i}\nabla+A)^2+V$ on a…
We consider the magnetic Schrodinger operator in a two-dimensional strip. On the boundary of the strip the Dirichlet boundary condition is imposed except for a fixed segment (window), where it switches to magnetic Neumann boundary condition…
We consider a Schr\"odinger operator H with a non-vanishing radial magnetic field B=dA and Dirichlet boundary conditions on the unit disk. We assume growth conditions on B near the boundary which guarantee in particular the compactness of…
We study the Schr\"odinger operator $L=-\Delta+V$ on a star-shaped domain $\Omega$ in $\mathbb{R}^d$ with Lipschitz boundary $\partial\Omega$. The operator is equipped with quite general Dirichlet- or Robin-type boundary conditions induced…
In this paper we study inverse boundary value problems with partial data for the magnetic Schr\"odinger operator. In the case of an infinite slab in $R^n$, $n\ge 3$, we establish that the magnetic field and the electric potential can be…
We study sufficient conditions for the absence of positive eigenvalues of magnetic Schr\"odinger operators in $\mathbb{R}^d,\, d\geq 2$. In our main result we prove the absence of eigenvalues above certain threshold energy which depends…
In this paper we consider magnetic Schroedinger operators on the two-dimensional unit disk with a radially symmetric magnetic field which explodes to infinity at the boundary. We prove a bound for the eigenvalue moments and a bound for the…