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The dimension of the Hilbert space needed for the description of aninteracting electron system increases exponentially with electron number $N$.As pointed out by W. Kohn this exponential wall problem (EWP) limits theconcept of many-electron wavefunctions based on solutions of Schr\"odinger'sequation to $N \leq N_0$, where $N_0 \approx 10^3$ \cite{Kohn1999}. Thislimitation does not hold when the electronic interactions are neglected ortreated in a mean-field approximation. The EWP has directed electronicstructure calculations for solids to methods like density-functional theorywhich avoid dealing with many-electron wavefunctions. We show that the highlyunsatisfactory limitation of many-electron wavefunctions to $N \leq N_0$ can beovercome by generalizing their definition. We show for the ground state of alarge system that it is the logarithm of the solution of Schr\"odinger'sequation which should be used to characterize this system. In this case thewavefunctions of independent subsystems add up rather than multiply. Thisfeature is realized by the action function. It provides a simple physicalpicture for the resolution of the EWP.

Role of the action function in defining electronic wavefunctions for large systems