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

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Abstract

The lowest eigenvalue of non-commutative harmonic oscillators Q(alpha,beta) (alpha > 0,beta > 0, alpha beta > 1) is studied. It is shown that Q(alpha,beta) can be decomposed into four self-adjoint operators, [GRAPHICS] and all the eigenvalues of each operator Q(sigma p) are simple. We show that the lowest eigenvalue of Q(alpha,beta) is simple whenever alpha not equal beta. Furthermore a Jacobi matrix representation of Q(sigma p) is given and spectrum of Q(sigma p) is considered numerically.

Journal

  • JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 415(2), 595-609, 2014-07-15

    ACADEMIC PRESS INC ELSEVIER SCIENCE

Codes

  • NII Article ID (NAID)
    120005468450
  • NII NACSIS-CAT ID (NCID)
    AA00252847
  • Text Lang
    ENG
  • Article Type
    journal article
  • Data Source
    IR 
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