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. A numerical illustration of the scheme is provided for the closed-shell atomic systems He, Be, and Ne in their ground state and for singlet electronic excited state for helium by calculating the Compton profiles and the expectation values derived from given coordinate-space electron densities.
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