Densities, density-functionals and electron fluids

This review article discusses, from a unified standpoint, three current approaches in applied quantum mechanics that adopt the single-particle density as a basic variable, viz. density-functional theory (DFT), quantum fluid dynamics (QFD) and study of the properties of a system through "local" quantities in three-dimensional (3D) space. First, the methodology of DFT is covered in detail with particular attention to the kinetic and exchange-correlation energy functionals. Next, recent applications of DFT to atoms, molecules, solids, nuclei and the liquid state are briefly described. Then, in course of the formulation and interpretation of QFD equations for one-and many-particle systems, various interesting features such as quantum streamlines, fluid vorticity and circulation, etc. are discussed. Applications of QFD to the study of collisions as well as electric and magnetic properties of many-electron systems and to the study of nuclear properties are subsequently described. Finally, the definition and usefulness of a property density in 3D space and certain interconnections between the above three approaches have been highlighted. A concerted attack on quantum systems through these three approaches should result in considerable additional insight into various physicochemical phenomena