Tuesday, April 23, 2013

1304.5578 (Fumio Hiroshima et al.)

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

Fumio Hiroshima, Itaru Sasaki
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.
View original: http://arxiv.org/abs/1304.5578

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