The integrated density of states for an interacting multielectron homogeneous model

TL;DR

This paper demonstrates that for a system of interacting electrons in a homogeneous potential, the integrated density of states remains the same as that of free electrons, provided the single-electron Hamiltonian has a density of states.

Contribution

It proves that the integrated density of states for an interacting multielectron system matches that of the free system under certain conditions.

Findings

The interacting Hamiltonian admits a density of states.

The integrated density of states of the interacting system coincides with the free system.

The result applies to systems with a homogeneous potential.

Abstract

For a system of n interacting electrons moving in the background of a "homogeneous" potential, we show that, if the single electron Hamiltonian admits a density of states, so does the interacting Hamiltonian. Moreover this integrated density of states coincides with that of the free electron Hamiltonian.