Transparent Potential Perturbations on Lattices and in the Periodical Structures. Elements of the Qualitative Theory of Wave Motion Over the Channels

It is shown that the peculiarities of the wave motion over the discrete variable 'n' do not permit to construct the local potential v(n) transparent for all energies of the allowed zone. Every local potential well bends the allowed zone in the plane 'E, n' and necessitates the lowering of its upper boundary (the appearance of the effective barrier hanging from above) what gives strong reflection of waves. To remove the hindering prominence of the forbidden zone into the allowed one it is possible to use the minimal nonlocality: the potential u(n) on the neighbour diagonals of the matrix finite-difference Hamiltonian. Together the soliton-like potentials constitute the reflectionless system. Different transparent systems are demonstrated by means of instructive illustrations. In the periodical potentials the matching conditions of functions on the neighbour intervals (periods) play the part of minimal nonlocality. (author). 31 refs., 6 figs