  The current burst in research activities on disordered semiconductors calls
for the development of appropriate theoretical tools that reveal the features
of electron states in random potentials while avoiding the time-consuming
numerical solution of the Schr\"odinger equation. Among various approaches
suggested so far, the low-pass filter approach of Halperin and Lax (HL) and the
so-called localization landscape technique (LLT) have received most recognition
in the community. We prove that the HL approach becomes equivalent to the LLT
for the specific case of a Lorentzian filter when applied to the Schr\"odinger
equation with a constant mass. Advantageously, the low-pass filter approach
allows further optimization beyond the Lorentzian shape. We propose the global
HL filter as optimal filter with only a single length scale, namely, the size
of the localized wave packets. As an application, we design an optimized
potential landscape for a (semi-)classical calculation of the number of
strongly localized states that faithfully reproduce the exact solution for a
random white-noise potential in one dimension.
