# Dresden 2020 – wissenschaftliches Programm

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# TT: Fachverband Tiefe Temperaturen

## TT 33: Correlated Electrons: Method Development 1

### TT 33.13: Vortrag

### Mittwoch, 18. März 2020, 12:45–13:00, HSZ 201

Wavefunctions for macroscopic electron systems — •Peter Fulde — Max-Planck-Institut für Physik komplexer Systeme

The dimensions of Hilbert space explode exponentially with number N of interacting electrons. Therefore, as stressed by W. Kohn [1], the concept of the many-electron wavefunction ψ (r_{1}, …, r_{N}) is in general not a legitimate scientific concept when N ≥ N_{0} where N_{0} is of order 10^{3}. The so called Exponential Wall Problem (EWP) does not exist though when the interactions are treated in a mean-field approximation, since then solving the Schrödinger equation reduces to a one-electron problem. It is easily seen that the EWP originates from the multiplicative form ψ_{AB} = ψ_{A} ⊗ ψ_{B} when two nearly coupled systems A and B are considered. This implies a high degree of information redundancy. In order to resolve the EWP when we want, e.g., to determine the electronic ground-state wavefunction of a periodic solid we have to find a representation in which the information redundancy is removed. It is shown how this is done and applied in practical calculations [2]. In essence the wavefunction is of a form corresponding to lnψ instead of ψ and therefore additive rather than multiplicative.

[1] W. Kohn: Rev. Mod. Phys. 71, 1253 (1999)

[2] P. Fulde: J. Chem. Phys. 150, 030901 (2019)