Abstract
Using a recently proposed kinetic energy density functional and an amalgamation of density functional theory with quantum fluid dynamics, a time-dependent Kohn-Sham-type equation in three-dimensional space, which is a new non-linear Schrödinger equation, has been derived. The equation is also derived through the stochastic interpretation of quantum mechanics. A molecular “thermodynamic” viewpoint is suggested in terms of space-time-dependent quantities. Numerical solution of the above equation yields the time-dependent charge density, current density, effective potential and chemical potential. Perspective plots of these quantities for the proton-neon 25 keV head-on collision are presented.
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