  The reason why the effective-mass approximation, derived for wave packets
constructed from infinite-periodic-systems' wave functions, works so well with
nanoscopic structures, has been an enigma and a challenge for theorists. To
explain and clarify this issue, we re-derive the effective-mass approximation
in the framework of the theory of finite periodic systems, i.e., using energy
eigenvalues and fast-varying eigenfunctions, obtained with analytical methods
where the finiteness of the number of primitive cells per layer, in the
direction of growth, is a prerequisite and an essential condition. This
derivation justifies and explains why the effective-mass approximation works so
well for nano-structures. We show also with explicit optical-response
calculations that the rapidly varying eigenfunctions
$\Phi_{\epsilon_0,\eta_0}(z)$ of the one-band wave functions
$\Psi^{\epsilon_0,\eta_0}_{\mu,\nu}(z)= \Psi^{\epsilon_0}_{\mu,\nu}(z)
\Phi_{\epsilon_0,\eta_0}(z)$, can be safely dropped out for the calculation of
inter-band transition matrix elements.
