Spectral analysis of non-commutative harmonic oscillators: The lowest eigenvalue and no crossing

Fumio Hiroshima, Itaru Sasaki

研究成果: ジャーナルへの寄稿記事

3 引用 (Scopus)

抄録

The lowest eigenvalue of non-commutative harmonic oscillators Q(α, β) (α>0, β>0, αβ>1) is studied. It is shown that Q(α, β) can be decomposed into four self-adjoint operators,Q(α,β)={N-ary circled plus operator}σ=±,p=1,2Qσp, and all the eigenvalues of each operator Qσp are simple. We show that the lowest eigenvalue of Q(α, β) is simple whenever α≠β. Furthermore a Jacobi matrix representation of Qσp is given and spectrum of Qσp is considered numerically.

元の言語英語
ページ(範囲)595-609
ページ数15
ジャーナルJournal of Mathematical Analysis and Applications
415
発行部数2
DOI
出版物ステータス出版済み - 7 15 2014

Fingerprint

Spectral Analysis
Harmonic Oscillator
Spectrum analysis
Lowest
Eigenvalue
Jacobi Matrix
Matrix Representation
Operator
Self-adjoint Operator

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

これを引用

Spectral analysis of non-commutative harmonic oscillators : The lowest eigenvalue and no crossing. / Hiroshima, Fumio; Sasaki, Itaru.

:: Journal of Mathematical Analysis and Applications, 巻 415, 番号 2, 15.07.2014, p. 595-609.

研究成果: ジャーナルへの寄稿記事

@article{d82773bd095b43998db343af03286ef9,
title = "Spectral analysis of non-commutative harmonic oscillators: The lowest eigenvalue and no crossing",
abstract = "The lowest eigenvalue of non-commutative harmonic oscillators Q(α, β) (α>0, β>0, αβ>1) is studied. It is shown that Q(α, β) can be decomposed into four self-adjoint operators,Q(α,β)={N-ary circled plus operator}σ=±,p=1,2Qσp, and all the eigenvalues of each operator Qσp are simple. We show that the lowest eigenvalue of Q(α, β) is simple whenever α≠β. Furthermore a Jacobi matrix representation of Qσp is given and spectrum of Qσp is considered numerically.",
author = "Fumio Hiroshima and Itaru Sasaki",
year = "2014",
month = "7",
day = "15",
doi = "10.1016/j.jmaa.2014.01.005",
language = "English",
volume = "415",
pages = "595--609",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "2",

}

TY - JOUR

T1 - Spectral analysis of non-commutative harmonic oscillators

T2 - The lowest eigenvalue and no crossing

AU - Hiroshima, Fumio

AU - Sasaki, Itaru

PY - 2014/7/15

Y1 - 2014/7/15

N2 - The lowest eigenvalue of non-commutative harmonic oscillators Q(α, β) (α>0, β>0, αβ>1) is studied. It is shown that Q(α, β) can be decomposed into four self-adjoint operators,Q(α,β)={N-ary circled plus operator}σ=±,p=1,2Qσp, and all the eigenvalues of each operator Qσp are simple. We show that the lowest eigenvalue of Q(α, β) is simple whenever α≠β. Furthermore a Jacobi matrix representation of Qσp is given and spectrum of Qσp is considered numerically.

AB - The lowest eigenvalue of non-commutative harmonic oscillators Q(α, β) (α>0, β>0, αβ>1) is studied. It is shown that Q(α, β) can be decomposed into four self-adjoint operators,Q(α,β)={N-ary circled plus operator}σ=±,p=1,2Qσp, and all the eigenvalues of each operator Qσp are simple. We show that the lowest eigenvalue of Q(α, β) is simple whenever α≠β. Furthermore a Jacobi matrix representation of Qσp is given and spectrum of Qσp is considered numerically.

UR - http://www.scopus.com/inward/record.url?scp=84896319701&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896319701&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2014.01.005

DO - 10.1016/j.jmaa.2014.01.005

M3 - Article

AN - SCOPUS:84896319701

VL - 415

SP - 595

EP - 609

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -