1. The problem statement, all variables and given/known data Suggest how the energy diﬀerence arises between the optic and acoustic branches in a 1d diatomic chain. 2. Relevant equations 3. The attempt at a solution I know that on the optic branch atoms oscillate in anti-phase within the unit cell and in phase in the unit cell on the acoustic branch. So does the energy difference come from the difference in energy between the symmetric and anti-symmetric wavefunctions required to describe the two situations? or does the extra energy in the optic branch come from the energy contained within the oscillating dipole that will be set up, or are these two answers intrinsically linked? any help much appreciated.