We show that the wave operators for Schrödinger scattering in $\mathbb{R}^4$ have a particular form which depends on the existence of resonances. As a consequence of this form, we determine the contribution of resonances to the index of the wave operator.
In heavy atoms and molecules, on the distances $a \gg Z^{-1}$ from all of the nuclei (with a charge $Z_m$) we prove that $ρ_Ψ(x)$ is approximated in $L^p$-norm, by the Thomas-Fermi density.
We extend a result of Davies and Nath on the location of eigenvalues of Schrödinger operators with slowly decaying complex-valued potentials to higher dimensions. In this context, we also discuss various examples related to the Laptev--Safronov conjecture.
This paper deals with the $L_p$-spectrum of Schrödinger operators on the hyperbolic plane. We establish Lieb-Thirring type inequalities for discrete eigenvalues and study their dependence on $p$. Some bounds on individual eigenvalues are derived as well.
We use the Hilbert distance on cones and the Birkhoff-Hopf Theorem to prove decay of correlation, analyticity of the free energy and a central limit theorem in the one dimensional Jellium model with non constant density charge background, both in the classical and quantum cases.
In this paper we study multipliers associated to the harmonic oscillator (also called Hermite multipliers) belonging to the ideal of $r$-nuclear operators on Lebesgue spaces. We also study the nuclear trace and the spectral trace of these operators.
Estimates for the total multiplicity of eigenvalues for Schrödinger operator are established in the case of compactly supported or exponentially decreasing complex-valued potential.
Old paper on the abstract scattering theory (ST) of periodic Hamiltonians. Updating of the references and correction of some minor non-mathematical misprints by H.C. Rosu.
An analogue of Rellich's theorem is proved for discrete Laplacian on square lattice, and applied to show unique continuation property on certain domains as well as non-existence of embedded eigenvalues for discrete Schr{ö}dinger operators.
Given an open real interval Δ and two selfadjoint operators A_1, A_2 in a Π_κ-space with n-dimensional resolvent difference we show that the difference of the total multiplicities of the eigenvalues of A_1 and A_2 in Δ is at most n+2κ.
We consider the inverse spectral problem for periodic Jacobi matrices in terms of the vertical slits on the quasi-momentum domain plus the Dirichlet eigenvalues, i.e., the Marchenko-Ostrovsky mapping. Moreover, we show that the gradients of the Dirichlet eigenvalues and of the so-called norming constants are linear independent.
For first order systems, we obtain an efficient bound on the exponential decay of an eigenfunction in terms of the distance between the corresponding eigenvalue and the essential spectrum. As an example, the Dirac operator is considered.
Inverse problem relatively domain for the plate under across vibrations is considered. The definition of s-functions is interoduced. The construction for defining of the domain of the plate by given s-functions is offered.
We define scattering phases associated to pairs of Laplacians on asymptotically hyperbolic manifolds, and prove some spectral asymptotics for them. These result are applications of Isozaki-Kitada's constructions which we adapt to this framework.