Asymptotic expansion of the integrated density of states of a two-dimensional periodic Schrodinger operator

TL;DR

This paper establishes the full asymptotic expansion of the integrated density of states for a two-dimensional Schrödinger operator with a smooth periodic potential, advancing understanding of spectral properties in quantum mechanics.

Contribution

It provides the first complete asymptotic expansion for the integrated density of states in this setting, filling a gap in spectral theory for periodic operators.

Findings

Complete asymptotic expansion derived

Advances spectral analysis of periodic Schrödinger operators

Provides tools for further spectral and quantum studies

Abstract

We prove the complete asymptotic expansion of the integrated density of states of a two-dimensional Schrodinger operator with a smooth periodic potential