2. A simple lattice with a two-dimensional square lattice, assuming that the atomic mass is M, the B lattice constant is a, and the restoring force constant of the nearest neighbor atom is The atomic vibration is assumed to be perpendicular to the plane of the atoms. Try to prove that the Mw2ẞ (2 cos qua- cos qua) lattice dispersion relation of two-dimensional system is = - 3. Consider the two-dimensional square lattice that consist of atoms with mass of m, and the lattice constant is a, taking into account only the interaction between the nearest neighbors, and the B restoring force constant is assumed that the phonon dispersion relation curve is 4ẞ m aq -(sin()) 2 (1) Under the long wavelength limit, find the density of the states of the phonon the number of lattice vibration in the unit frequency interval; D(w) that is, '