  Wavefunctions for large electron numbers $N$ are plagued by the Exponential
Wall Problem (EWP), i.e., an exponential increase in the dimensions of Hilbert
space with $N$. Therefore they loose their meaning for macroscopic systems, a
point stressed in particular by W. Kohn. The EWP has to be resolved in order to
be able to perform electronic structure calculations, e.g., for solids. The
origin of the EWP is the multiplicative property of wavefunctions when
independent subsystems are considered. Therefore it can only be avoided when
wavefunctions are formulated so that they are additive instead, in particular
when matrix elements involving them are calculated. We describe how this is
done for the ground state of a macroscopic electron system. Going over from a
multiplicative to an additive quantity requires taking a logarithm. Here it
implies going over from Hilbert space to the operator- or Liouville space with
a metric based on cumulants. The operators which define the ground-state
wavefunction generate fluctuations from a mean-field state. The latter does not
suffer from an EWP and therefore may serve as a vacuum state. The fluctuations
have to be {\it connected} like the ones caused by pair interactions in a
classical gas when the free energy is calculated (Meyer's cluster expansion).
This fixes the metric in Liouville space. The scheme presented here provides a
solid basis for electronic structure calculations for the ground state of
solids. In fact, its applicability has already been proven. We discuss also
matrix product states, which have been applied to one-dimensional systems with
results of high precision. Although these states are formulated in Hilbert
space they are processed by using operators in Liouville space. We show that
they fit into the general formalism described above.
