Diploma thesis

5 Outlook
We tried on the one hand several expressions and possible real valued functions for ψ for this
approach and on the other hand piecewise defined wave functions including a Gauss function in
area 1 and 3 and a polynomial in area 2 but neither the variation of the real and the imaginary
part nor of the absolute value yield satisfying results for the non-interacting density.
The fact that we are able to reproduce the densities with such an ansatz for c = 0, that is for the
real case, implies that the complexness of the system is responsible for the non-applicability of
this particular variational approach.
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