therefore antisymmetrical waves form the binding energy effectively quantized particles form bloch waves in insulators effectively metal fermions form bloch waves in the alkali metals on the contrary atomic vibrations can be considered as standing waves by anology quantized waves are transformed along lattice directions because of equipartition normal modes can be calculated by perturbation theory however phonons suffer electron-phonon interactions however electrons are propogated along the crystal axes hence electrons produce reflections in the 19th century Lorentz failed to explain the Rydberg constant in the 19th century Lorentz explained solids mathematically in 1869 J. J. Thomson proceeded wrongly with distinguishable particles in 1928 Brioullin tackled the problem using Schrodinger's equation recently Born and Von Karman considered solids with this in mind before the war Brioullin predicted the energy gaps