Quantum Theory of Non-Homogeneous Phases of Helium

of the art in conventional variational theories. We introduce then the Shadow Wave Function (SWF) in its original formulation, and its extension to Local Density Shadow Wave Function (LD-SvVF), developed in order to describe inhomogeneous systems such as liquid-solid coexistence. vVe will then present results on the spontaneous crystallization of a superdense liquid sample using such formalism, on the study of the solid-liquid coexistence and interface in 4He Finally preliminary results on the extension of SWF to 3He.