  The dimension of the Hilbert space needed for the description of an
interacting electron system increases exponentially with electron number $N$.
As pointed out by W. Kohn this exponential wall problem (EWP) limits the
concept of many-electron wavefunctions based on solutions of Schr\"odinger's
equation to $N \leq N_0$, where $N_0 \approx 10^3$ \cite{Kohn1999}. This
limitation does not hold when the electronic interactions are neglected or
treated in a mean-field approximation. The EWP has directed electronic
structure calculations for solids to methods like density-functional theory
which avoid dealing with many-electron wavefunctions. We show that the highly
unsatisfactory limitation of many-electron wavefunctions to $N \leq N_0$ can be
overcome by generalizing their definition. We show for the ground state of a
large system that it is the logarithm of the solution of Schr\"odinger's
equation which should be used to characterize this system. In this case the
wavefunctions of independent subsystems add up rather than multiply. This
feature is realized by the action function. It provides a simple physical
picture for the resolution of the EWP.
