Asymptotic expansion of the spectrum for periodic Schrödinger operators

2022/09/25 by Armstrong, Scott, Venkatraman, Raghavendra
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.12220

Abstract

We prove an asymptotic expansion for the eigenvalues and eigenfunctions of Schrödinger-type operator with a confining potential and with principle part a periodic elliptic operator in divergence form. We compare the spectrum to the homogenized operator and characterize the corrections up to arbitrarily high order.

Related

• Asymptotic Analysis of the Periodic Schrodinger Operator
• On the eigenvalues for slowly varying perturbations of a periodic Schrödinger operator
• Spectral shift function for slowly varying perturbation of periodic Schroedinger operators
• Spectral shift function for perturbed periodic Schroedinger operators. The large-coupling constant limit case
• An overview of periodic elliptic operators