Local Density Approximation of Bose-Einstein Condensation

3 Local Density Approximation of Bose-Einstein Condensation 

In order Eq. (1.184) may be further worked out the form of the interaction function should be specified it act as an inter-particle interaction energy, being thus related with the inter-particle bilocal potential itself in fact it was found having the functional form (Vetter, 1997 Putz, 2011b-c, 2012a,c)  

Quantum Nanochemistry—Volume III Quantum Molecules and Reactivity 

However, as usually in DFT, but also due to the special feature of the BEC being localized in a narrow region of space, the custom local density approximation may be also here implemented by imposing the bilocal-to-local transformation of the interaction upon the order parameter s delta function dependency 

Further replacement of the fluctuation density KS-average by the global prescription given by Eq. (1.157), while vanishing the fluctuation itself, transforms Eq. (1.188) successively as 

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