On a discrete Schrödinger equation for a quantum dot with a nonlocal potential

The paper considers the discrete Schrödinger equation. This is the characteristic equation for a Schrödinger operator of a certain type. It corresponds to a mathematical model that describes nanoscale devices that regulate electron transport using, for example, the Aharonov–Bohm effect. We study the general spectral properties of the operator, find eigenvalues and resonances, and investigate the scattering problem. In particular, conditions for complete transmission (i.e., transmission with probability equal to one) are found, and the possibility of Fano resonance is indicated.