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

Fumio Hiroshima, Itaru Sasaki

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)595-609
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Volume415
Issue number2
DOIs
Publication statusPublished - Jul 15 2014

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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