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

Fumio Hiroshima, Itaru Sasaki

    Research output: Contribution to journalArticlepeer-review

    5 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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