Abstract
The point canonical transformations map the Schrodinger equation with constant mass to a wave equation with a position-dependent effective mass. Using such a technique we derive, for a one-dimensional inhomogeneous system of noninteracting fermions with density ρ(x) and spatially dependent effective mass distribution m(x), the semiclassical kinetic energy density functional τ(ρ) in the so-called extended Thomas–Fermi model up to order 2. For a given position-dependent mass, we compare numerically the total semiclassical kinetic energy with its exact quantum mechanical counterpart. The qualitative agreement is excellent.
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