  We extend previous work applying elementary matrix mechanics to
one-dimensional periodic arrays (to generate energy bands) to two-dimensional
arrays. We generate band structures for the square lattice "2D Kronig-Penney
model" (square wells), muffin-tin potential (cylindrical wells), and Gaussian
wells. We then apply the method to periodic arrays of more than one atomic site
in a unit cell, in particular, the case of materials with hexagonal lattices
like graphene. These straightforward extensions of undergraduate-level
calculations allow students to readily determine band structures of current
research interest.
