Since it is rather hard to extract physical results out of the multi-particle Hamiltonian it's difficult to decide wether it includes all real electronic effects. But at least such an important effect like superconductivity which is a quite common effect for metals at temperatures low enough cannot be explained by a description which completely separates the electronic and ionic degrees of freedom because quantities characteristic for superconductivity depend on the stiffness of the crystal. This leads to the necessity of taking into account electron-phonon interaction.