Do We Know the Ground State Wave Function in Density Functional Theory

4 Do We Know the Ground State Wave Function in Density Functional Theory  

From a purist theoretical point of view, there is one further important result hidden in the Levy constrained-search strategy it provides a unique, albeit only formal, route to extract the ground state wave function F, from the ground state density p0. This is anything but a trivial problem, since there are many antisymmetric N-electron wave functions that yield 

11 Even though the correct many electron wave function is not available inDFT, we will see in Section 5.3.3 that a related wave function exists, which can often be used for qualitative interpretation. 

Similarly, the constrained-search scheme, even though being very elegant in appearance and strong in formal power, is only of theoretical value and offers no solution to practical considerations. Simply, the program indicated in Section 4.3 cannot be realized - how would we ever be able to search through all wave functions Since this is obviously impossible, setting up the functional F[p] = min ( F T + Vee F is impossible, too. A second 

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