New sum rules for an electron in a periodic or nearly periodic potential

TL;DR

This paper derives novel sum rules for electronic oscillator strengths in periodic potentials, revealing a new physical principle akin to spectroscopic stability in solid-state physics.

Contribution

It introduces new sum rules applicable within and between energy bands, based on a solid-state analogue of spectroscopic stability, differing from traditional sum rules.

Findings

Sum rules apply within a single energy band.

Sum rules also apply between different bands.

Physical origin linked to a solid-state spectroscopic stability principle.

Abstract

I derive new sum rules for the electronic oscillator strengths in a periodic or nearly periodic potential, which apply within a single energy band and between any two bands. The physical origin of these sum rules is quite unlike that of conventional sum rules, and is shown to be associated with a solid-state counterpart to the principle of spectroscopic stability known in atomic physics.