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We demonstrate using the classical density functional theory (DFT) model thatan intermediate degree of mass localization in the amorphous state is essentialfor producing the boson peak. The localization length $\ell$ is identified fromthe width of the gaussian density profile in terms of which the inhomogeneousdensity 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 masslocalization in the amorphous state. For more delocalized states($\ell>\ell_0$) occurrence of boson peak is unfeasible.

Localization, disorder and boson peak in an amorphous solid