ASYMPTOTIC EXPANSION OF THE SPECTRUM FOR PERIODIC SCHRODINGER OPERATORS

Scott Armstrong; Raghavendra Venkatraman

doi:10.1137/22M1526228

ASYMPTOTIC EXPANSION OF THE SPECTRUM FOR PERIODIC SCHRODINGER OPERATORS

Scott Armstrong, Raghavendra Venkatraman

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English (US)
Pages (from-to)	1770-1808
Number of pages	39
Journal	SIAM Journal on Mathematical Analysis
Volume	56
Issue number	2
DOIs	https://doi.org/10.1137/22M1526228
State	Published - 2024

Keywords

homogenization
Schrodinger
spectrum

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

Access to Document

10.1137/22M1526228

Cite this

@article{d1191e8bf8a44c58bb01015bdaf2400c,

title = "ASYMPTOTIC EXPANSION OF THE SPECTRUM FOR PERIODIC SCHRODINGER OPERATORS",

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

keywords = "homogenization, Schrodinger, spectrum",

author = "Scott Armstrong and Raghavendra Venkatraman",

year = "2024",

doi = "10.1137/22M1526228",

language = "English (US)",

volume = "56",

pages = "1770--1808",

journal = "SIAM Journal on Mathematical Analysis",

issn = "0036-1410",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "2",

}

TY - JOUR

T1 - ASYMPTOTIC EXPANSION OF THE SPECTRUM FOR PERIODIC SCHRODINGER OPERATORS

AU - Armstrong, Scott

AU - Venkatraman, Raghavendra

PY - 2024

Y1 - 2024

N2 - We prove an asymptotic expansion for the eigenvalues and eigenfunctions of Schrodinger-type operator with a confining potential and with the principle part of a periodic elliptic operator in divergence form. We compare the spectrum to the homogenized operator and characterize the corrections up to arbitrarily high order.

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

KW - homogenization

KW - Schrodinger

KW - spectrum

UR - http://www.scopus.com/inward/record.url?scp=85186962500&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85186962500&partnerID=8YFLogxK

U2 - 10.1137/22M1526228

DO - 10.1137/22M1526228

M3 - Article

AN - SCOPUS:85186962500

SN - 0036-1410

VL - 56

SP - 1770

EP - 1808

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 2

ER -

ASYMPTOTIC EXPANSION OF THE SPECTRUM FOR PERIODIC SCHRODINGER OPERATORS

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this