2013/04/20 by Fumio Hiroshima, Hiroshima, Fumio, Itaru Sasaki +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1304.5578
4figures. We revised section 3
arxiv created 2013/06/12 · arxiv updated 2013/06/14
The lowest eigenvalue of non-commutative harmonic oscillators Q is studied. It is shown that Q can be decomposed into four self-adjoint operators, and all the eigenvalues of each operator are simple. We show that the lowest eigenvalue E of Q is simple. Furthermore a Jacobi matrix representation of Q is given and spectrum of Q is considered numerically.