The Spectral Shift Function and The Friedel Sum Rule

TL;DR

This paper explores the connection between the spectral shift function and the Friedel sum rule in potential scattering theory, providing a new construction of the spectral shift function that confirms its role in the sum rule.

Contribution

It introduces an alternative construction of the spectral shift function and proves its validity in deriving the Friedel sum rule.

Findings

New construction of the spectral shift function

Validation of the spectral shift function in the Friedel sum rule

Clarification of the relationship between spectral shift and excess charge

Abstract

We study the relationship between the spectral shift function and the excess charge in potential scattering theory. Although these quantities are closely related to each other, they have been often formulated in different settings so far. Here we first give an alternative construction of the spectral shift function, and then we prove that the spectral shift function thus constructed yields the Friedel sum rule.