A trigonometric sum relevant to the nonrelativistic theory of atoms

A. Córdoba; C. Fefferman; L. Seco

doi:10.1073/pnas.91.13.5776

A trigonometric sum relevant to the nonrelativistic theory of atoms

A. Córdoba, C. Fefferman, L. Seco

Mathematics

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

6 Scopus citations

Abstract

We extend Van der Corput's method for exponential sums to study an oscillatory term appearing in the quantum theory of large atoms. We obtain an interpretation in terms of classical dynamics and we produce sharp asymptotic upper and lower bounds for the oscillations.

Original language	English (US)
Pages (from-to)	5776-5778
Number of pages	3
Journal	Proceedings of the National Academy of Sciences of the United States of America
Volume	91
Issue number	13
DOIs	https://doi.org/10.1073/pnas.91.13.5776
State	Published - Jun 21 1994

All Science Journal Classification (ASJC) codes

General

Keywords

Weyl sums
quantum mechanics
trace formulas

Access to Document

10.1073/pnas.91.13.5776

Cite this

@article{92776d6dfec24506805201739bf0fff4,

title = "A trigonometric sum relevant to the nonrelativistic theory of atoms",

abstract = "We extend Van der Corput's method for exponential sums to study an oscillatory term appearing in the quantum theory of large atoms. We obtain an interpretation in terms of classical dynamics and we produce sharp asymptotic upper and lower bounds for the oscillations.",

keywords = "Weyl sums, quantum mechanics, trace formulas",

author = "A. C{\'o}rdoba and C. Fefferman and L. Seco",

year = "1994",

month = jun,

day = "21",

doi = "10.1073/pnas.91.13.5776",

language = "English (US)",

volume = "91",

pages = "5776--5778",

journal = "Proceedings of the National Academy of Sciences of the United States of America",

issn = "0027-8424",

publisher = "National Academy of Sciences",

number = "13",

}

TY - JOUR

T1 - A trigonometric sum relevant to the nonrelativistic theory of atoms

AU - Córdoba, A.

AU - Fefferman, C.

AU - Seco, L.

PY - 1994/6/21

Y1 - 1994/6/21

N2 - We extend Van der Corput's method for exponential sums to study an oscillatory term appearing in the quantum theory of large atoms. We obtain an interpretation in terms of classical dynamics and we produce sharp asymptotic upper and lower bounds for the oscillations.

AB - We extend Van der Corput's method for exponential sums to study an oscillatory term appearing in the quantum theory of large atoms. We obtain an interpretation in terms of classical dynamics and we produce sharp asymptotic upper and lower bounds for the oscillations.

KW - Weyl sums

KW - quantum mechanics

KW - trace formulas

UR - http://www.scopus.com/inward/record.url?scp=0028237285&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028237285&partnerID=8YFLogxK

U2 - 10.1073/pnas.91.13.5776

DO - 10.1073/pnas.91.13.5776

M3 - Article

C2 - 11607477

AN - SCOPUS:0028237285

SN - 0027-8424

VL - 91

SP - 5776

EP - 5778

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 13

ER -

A trigonometric sum relevant to the nonrelativistic theory of atoms

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this