  A quantum-mechanical model of Cu-O-Cu-O four-center four-electron part of the
copper-oxide plane embedded in a superconducting crystal La$_{2-x}$Sr$%
_{x}$CuO$_{4}$ (LSCO) is considered. It is shown that displacing the
nearest-neighbor La(Sr)O plane lattice atoms off by a distance as small as $\pm
0.1$ angstrem, i.e. of the order of ground state vibrations dictated by the
Heisenberg uncertainty principle, may trigger a dramatic change of the ground
state electronic charge distribution in the CuOCuO system. This results in the
electron pairs' concerted sliding within the system over distances about 2
angstrem , i.e. close to the copper oxygen atomic distance. The effect depends
crucially on the lattice crystal field and doping. The appearance of energy
gaps associated with the electronic states' avoided crossings points to a
universal nature of the phenomenon. The results suggest a generalization of the
models used up to now in description of strongly correlated electrons.
