Spectral analysis of non-commutative harmonic oscillators: The lowest eigenvalue and no crossing
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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 OF MATHEMATICAL ANALYSIS AND APPLICATIONS
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 415(2), 595-609, 2014-07-15
ACADEMIC PRESS INC ELSEVIER SCIENCE