Abstract
Adopting a simple independent 'particle in a box' model with a finite square barrier, Dirac's relativistic wave equation has been used to obtain exact results for the electron density and kinetic energy density in the semi-infinite inhomogeneous electron-gas limit. By utilising a suitable power series development, one can pass to the non-relativistic limit and subsequently to the limit of an infinite barrier, in which case well established results are regained. Finally, the relation to relativistic Thomas-Fermi theory is discussed.
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