We investigate the validity and limitations of the envelope-function a
pproximation (EFA), widely accepted for the description of the electro
nic states of semiconductor heterostructures. We consider narrow quant
um wells of GaAs confined by AlxGa1-xAs barriers. Calculations perform
ed within the tight-binding approxima tion using ensembles of supercel
ls are compared to the EFA results. Results for miniband widths in sup
erlattices obtained in different approximations are also discussed. Th
e main source of discrepancy for narrow wells is the treatment of allo
y disorder within the virtual crystal approximation. We also test the
two key assumptions of the EFA: (a) that the electronic wave functions
have Bloch symmetry with well-defined (k) over right arrow in the all
oy region; (b) that the periodic parts of the Bloch functions are the
same throughout the heterostructure. We show that inaccuracies are mai
nly due to the former assumption.