The k . p method + envelope function combination used for semiconducto
r heterostructures is based on approximations dubious under some condi
tions. We directly compare 8-band k . p with pseudopotential results f
or [001] GaAs/AlAs superlattices and quantum wells with all k . p inpu
t parameters directly computed from bulk GaAs and AlAs pseudopotential
bands. We find generally very good agreement for zone-center hole sta
tes within similar to 200 meV of the GaAs valence band maximum, but i)
systematic errors deeper in the valence band and ii) qualitative erro
rs for even the lowest conduction bands with appreciable contributions
from off-Gamma zinc-blende states. We trace these errors to inadequat
e k . p description of bulk GaAs and AlAs band dispersion away from th
e zone center.