Negative Eigenvalues of Two-Dimensional Schrödinger Operators

Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields

Solvable Two - Dimensional Schrödinger

S.P.Novikov: University of Maryland at College Park, Department of Mathematics and IPST, College Park MD 20742-2431 USA and Landau Institute for Theoretical Physics, Moscow 117940, Kosygin street 2, Russia. E-mail adress [email protected] A.P.Veselov: Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK and Department of Mathematics and Mec...

Small graphs with exactly two non-negative eigenvalues

Let $G$ be a graph with eigenvalues $lambda_1(G)geqcdotsgeqlambda_n(G)$. In this paper we find all simple graphs $G$ such that $G$ has at most twelve vertices and $G$ has exactly two non-negative eigenvalues. In other words we find all graphs $G$ on $n$ vertices such that $nleq12$ and $lambda_1(G)geq0$, $lambda_2(G)geq0$ and $lambda_3(G)0$, $lambda_2(G)>0$ and $lambda_3(G)

Convergence of Schrödinger Operators

For a large class, containing the Kato class, of real-valued Radon measures m on R the operators −∆ + ε∆ + m in L(R, dx) tend to the operator −∆ +m in the norm resolvent sense, as ε tends to zero. If d ≤ 3 and a sequence (μn) of finite real-valued Radon measures on R converges to the finite real-valued Radon measure m weakly and, in addition, supn∈N μ ± n (R) < ∞, then the operators −∆ + ε∆ + μ...

On the number of eigenvalues of Schrödinger operators with complex potentials

We study the eigenvalues of Schrödinger operators with complex potentials in odd space dimensions. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity.