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

Fumio Hiroshima; Itaru Sasaki

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

Mathematical Physics 2013-06-14 v2 math.MP

Authors: Fumio Hiroshima , Itaru Sasaki

Abstract

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.

Keywords

non-commutative harmonic oscillator spectral analysis lowest eigenvalue self-adjoint operator simple eigenvalue Jacobi matrix no crossing

Cite

@article{arxiv.1304.5578,
  title  = {Spectral analysis of non-commutative harmonic oscillators: the lowest eigenvalue and no crossing},
  author = {Fumio Hiroshima and Itaru Sasaki},
  journal= {arXiv preprint arXiv:1304.5578},
  year   = {2013}
}

Comments

4figures. We revised section 3

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

Abstract

Keywords

Cite

Comments

Related papers