Bound states of Schrodinger-type operators on one and two dimensional lattices

[摘要] We study the spectral properties of the Schrodinger-type operator (H) over cap (mu) := (H) over cap (0) + mu(V) over cap, mu >= 0, associated to a one-particle system in d-dimensional lattice Z(d), d = 1, 2, where the non-perturbed operator (H) over cap (0) is a self-adjoint convolution-type operator generated by a Hopping matrix (e) over cap: Z(d) -> Cand the potential (V) over cap is the multiplication operator by (v) over cap: Z(d) -> R. Under certain regularity assumption on (e) over cap and a decay assumption on (v) over cap, we establish the existence or non-existence and also the finiteness of eigenvalues of (H) over cap (mu). Moreover, in the case of existence we study the asymptotics of eigenvalues of (H) over cap (mu)as mu SE arrow 0. (C) 2021 The Author(s). Published by Elsevier Inc.

[发布日期] 2021-11-01

[关键词] Lattice;Eigenvalue;Essential spectrum;Coupling constant;Asymptotics