On negative eigenvalues of two-dimensional Schrödinger operators with singular potentials

Schrödinger Operators with Singular Potentials †

We describe classical and recent results on the spectral theory of Schrödinger and Pauli operators with singular electric and magnetic potentials

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.

Schrödinger operators with oscillating potentials ∗

Schrödinger operators H with oscillating potentials such as cos x are considered. Such potentials are not relatively compact with respect to the free Hamiltonian. But we show that they do not change the essential spectrum. Moreover we derive upper bounds for negative eigenvalue sums of H.

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

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)