ar X iv : m at h - ph / 0 40 90 74 v 2 2 5 Ja n 20 05 SCHRÖDINGER OPERATORS WITH FEW BOUND STATES

ar X iv : m at h - ph / 0 20 10 06 v 2 1 5 Ja n 20 02 Quasi - classical versus non - classical spectral asymptotics for magnetic Schrödinger operators with decreasing electric potentials

We consider the Schrödinger operator H on L 2 (R 2) or L 2 (R 3) with constant magnetic field, and electric potential V which typically decays at infinity exponentially fast or has a compact support. We investigate the asymptotic behaviour of the discrete spectrum of H near the boundary points of its essential spectrum. If the decay of V is Gaussian or faster, this behaviour is non-classical in...

ar X iv : m at h - ph / 0 50 10 33 v 1 1 2 Ja n 20 05 Indefinite metric

ar X iv : 0 90 5 . 09 74 v 1 [ m at h - ph ] 7 M ay 2 00 9 Symmetries and resonance sets for δ ′ - interactions July 20 , 2009

The symmetry properties of the family of δ ′-interactions with a resonant non-zero transparency resulting in non-separated states are discussed. It is shown that the connection matrix for these physically motivated interactions and the corresponding family of self-adjoint extensions can be constructed in a self-consistent way if the product δ ′ (x)ψ(x), where ψ(x) is a discontinuous wavefunctio...

ar X iv : m at h / 06 01 74 3 v 1 [ m at h . SP ] 3 0 Ja n 20 06 DETERMINANTS OF ZEROTH ORDER OPERATORS

ar X iv : m at h - ph / 9 90 70 23 v 1 2 8 Ju l 1 99 9 EIGENFUNCTIONS , TRANSFER MATRICES , AND ABSOLUTELY CONTINUOUS SPECTRUM OF ONE - DIMENSIONAL SCHRÖDINGER OPERATORS

In this paper, we will primarily discuss one-dimensional discrete Schrödinger operators (hu)(n) = u(n + 1) + u(n − 1) + V (n)u(n) (1.1D) on ℓ 2 (Z) (and the half-line problem, h + , on ℓ 2 ({n ∈ Z | n > 0}) ≡ ℓ 2 (Z +)) with u(0) = 0 boundary conditions. We will also discuss the continuum analog (Hu)(x) = −u ′′ (x) + V (x)u(x) (1.1C) on L 2 (R) (and its half-line problem, H + , on L 2 (0, ∞) wi...