  A novel method for the calculation of the energy dispersion relation (EDR)
and density of states (DOS) in one (1D) and two (2D) dimensions is introduced
and applied to linear lattices (1D) and square and hexagonal lattices (2D). The
(van Hove) singularities and (Dirac) zeros of the DOS are discussed. Results
for the 2D hexagonal lattice (graphene-like materials) are compared with
experimental data in microwave photonic crystals.
