Simple heterostructure models are often employed due to their computational
efficiency. The approximations involved are not, however, well understood;
this is particularly true with respect to the interfaces. In order to clar
ify this situation we study two different monoatomic (single-band) models a
nd two different diatomic (two-band) models all having identical dispersion
relations. We study in detail the relationships between the one- and two-b
and models, showing that their points of agreement and disagreement arise d
irectly from the handling of the interfaces. [S0163-1829(99)01111-X].