Quantum Potential for Diffraction and Exchange Effects

TL;DR

This paper develops effective quantum potentials to incorporate diffraction and exchange effects in semi-classical models of an ideal Fermi gas interacting with an impurity, extending existing potentials to better capture quantum phenomena.

Contribution

It generalizes the Kelbg potential to include both diffraction and degeneracy effects, providing a more comprehensive semi-classical approach for quantum systems.

Findings

Derived a generalized quantum potential for electron-impurity interactions.

Showed the electron-electron quantum potential aligns with previous exchange effect models.

Enhanced semi-classical modeling accuracy for quantum gases.

Abstract

Semi-classical methods of statistical mechanics can incorporate essential quantum effects by using effective quantum potentials. An ideal Fermi gas interacting with an impurity is represented by a classical fluid with effective electron-electron and electron-impurity quantum potentials. The electron-impurity quantum potential is evaluated at weak coupling, leading to a generalization of the Kelbg potential to include both diffraction and degeneracy effects. The electron-electron quantum potential for exchange effects only is the same as that discussed earlier by others.