@article{oai:soar-ir.repo.nii.ac.jp:00011723,
 author = {Hiroshima,  Fumio and Sasaki,  Itaru},
 issue = {2},
 journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
 month = {Jul},
 note = {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., Article, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 415(2):595-609 (2014)},
 pages = {595--609},
 title = {Spectral analysis of non-commutative harmonic oscillators: The lowest eigenvalue and no crossing},
 volume = {415},
 year = {2014}
}