  We demonstrate using the classical density functional theory (DFT) model that
an intermediate degree of mass localization in the amorphous state is essential
for producing the boson peak. The localization length $\ell$ is identified from
the width of the gaussian density profile in terms of which the inhomogeneous
density n(x) of the solid is expressed in DFT. At a fixed average density,
there exists a limiting value $\ell_0$ of $\ell$ signifying a minimum mass
localization in the amorphous state. For more delocalized states
($\ell>\ell_0$) occurrence of boson peak is unfeasible.
