  Electron density and electron momentum density, while independently tractable
experimentally, bear no direct connection without going through the
many-electron wave function. However, invoking a variant of the
constrained-search formulation of density functional theory, we develop a
general scheme (valid for arbitrary external potentials) yielding decent
momentum space properties, starting exclusively from the coordinate space
electron density. Numerical illustration of the scheme is provided for the
closed-shell atomic systems He, Be and Ne and for $1s^1~2s^1$ singlet
electronic excited state for Helium by calculating the Compton profiles and the
$<p^n>$ expectation values derived from given coordinate space electron
densities.
