Derivation of von Weizsäcker Equation Based on Green-Gauss Theorem

Z. Romanowski Interdisciplinary Centre for Materials Modelling, Pawińskiego 5a, 02-106 Warsaw, Poland

and S. Krukowski Institute of High Pressure Physics of the Polish Academy of Sciences, Sokołowska 29/37, 01-142 Warsaw, Poland

Received: August 19, 2008; Revised version: October 19, 2008;

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A simple and short derivation of von Weizsäcker equation for kinetic energy functional is presented. The derivation is based on the Green-Gauss theorem and is valid for one-electron systems. In the proof the asymptotic behavior of wave function for the finite systems was used. Two results important for kinetic energy functional evaluation are also derived as consequences of the Green-Gauss theorem.

DOI: 10.12693/APhysPolA.115.653 PACS numbers: 31.15.E-, 71.15.Mb, 71.15.Dx