In solid state physics, a proof of bearing energy gaps in one-dimesional dispersion relations is given by a quantum-mechanical perturbative approach applied to the level belonging to two bands at once, that is twice degenerate. For example for k=pi/a there's one of these levels between n=0 band and n=-1 band. The method is able to make visible the reason for which lower level is going lower again and upper, upper itself. I read somewhere that passing to tridimensional problem is not clever, not for a computational subject, but for the intrinsic long range property of electron-electron and electron-ion interactions. They go like 1/x. Now, here's my question: Should I deal with Fourier trasforms to reach some kind of a comprehension of this inability? They should go like 1/k^2, too slow to compensate in k-space (i.e. N-space) the fast growth of sites number: the volume of infinitesimal spherical shell N^2dN. If so, where's the cause? Thanks for your paid attention.