Add to ORKGWe show that whole-line Schrödinger operators with finitely many bound states have no embedded singular spectrum. In contradistinction, we show that embedded singular spectrum is possible even when the bound states approach the essential spectrum exponentially fast. We also prove the following result for one- and two-dimensional Schrödinger operators, H, with bounded positive ground states: Given a potential V, if both H±V are bounded from below by the ground-state energy of H, then V≡0
We consider Schrödinger operators of the form HR=−{d}2/{d}x2+q+iγχ[0,R] for large R>0 , where q∈L...
We consider Schrödinger operators of the form HR=−{d}2/{d}x2+q+iγχ[0,R] for large R>0 , where q∈L...
AbstractOur goal is to show that large classes of Schrödinger operatorsH=−Δ+VinL2(Rd) exhibit interv...
We show that whole-line Schrödinger operators with finitely many bound states have no embedded singu...
We show that whole-line Schrödinger operators with finitely many bound states have no embedded singu...
We consider discrete one-dimensional Schrödinger operators whose potentials decay asymptotically lik...
The relation between Hausdorff dimension of the singular spectrum of a Schrödinger operator and the ...
Let H be a one-dimensional discrete Schrödinger operator. We prove that if Σ_(ess)(H)⊂[−2,2], then H...
AbstractFor a large class of multi-dimensional Schrödinger operators it is shown that the absolutely...
It is well-known that for usual Schrödinger operators weakly coupled bound states exist in dimension...
In this note we provide an explicit lower bound on the spectral gap of one-dimensional Schr\"odinger...
AbstractWe consider spectral properties of a Schrödinger operator perturbed by a potential vanishing...
AbstractWe obtain conditions on the negative spectra of Schrödinger operators with potentials V and ...
In this paper we discuss several examples of Schrödinger operators describing a particle confined to...
In this paper we discuss several examples of Schrödinger operators describing a particle confined to...
We consider Schrödinger operators of the form HR=−{d}2/{d}x2+q+iγχ[0,R] for large R>0 , where q∈L...
We consider Schrödinger operators of the form HR=−{d}2/{d}x2+q+iγχ[0,R] for large R>0 , where q∈L...
AbstractOur goal is to show that large classes of Schrödinger operatorsH=−Δ+VinL2(Rd) exhibit interv...
We show that whole-line Schrödinger operators with finitely many bound states have no embedded singu...
We show that whole-line Schrödinger operators with finitely many bound states have no embedded singu...
We consider discrete one-dimensional Schrödinger operators whose potentials decay asymptotically lik...
The relation between Hausdorff dimension of the singular spectrum of a Schrödinger operator and the ...
Let H be a one-dimensional discrete Schrödinger operator. We prove that if Σ_(ess)(H)⊂[−2,2], then H...
AbstractFor a large class of multi-dimensional Schrödinger operators it is shown that the absolutely...
It is well-known that for usual Schrödinger operators weakly coupled bound states exist in dimension...
In this note we provide an explicit lower bound on the spectral gap of one-dimensional Schr\"odinger...
AbstractWe consider spectral properties of a Schrödinger operator perturbed by a potential vanishing...
AbstractWe obtain conditions on the negative spectra of Schrödinger operators with potentials V and ...
In this paper we discuss several examples of Schrödinger operators describing a particle confined to...
In this paper we discuss several examples of Schrödinger operators describing a particle confined to...
We consider Schrödinger operators of the form HR=−{d}2/{d}x2+q+iγχ[0,R] for large R>0 , where q∈L...
We consider Schrödinger operators of the form HR=−{d}2/{d}x2+q+iγχ[0,R] for large R>0 , where q∈L...
AbstractOur goal is to show that large classes of Schrödinger operatorsH=−Δ+VinL2(Rd) exhibit interv...