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

Fumio Hiroshima, Itaru Sasaki

3 引用 (Scopus)

### 抄録

The lowest eigenvalue of non-commutative harmonic oscillators Q(α, β) (α>0, β>0, αβ>1) is studied. It is shown that Q(α, β) can be decomposed into four self-adjoint operators,Q(α,β)={N-ary circled plus operator}σ=±,p=1,2Qσp, and all the eigenvalues of each operator Qσp are simple. We show that the lowest eigenvalue of Q(α, β) is simple whenever α≠β. Furthermore a Jacobi matrix representation of Qσp is given and spectrum of Qσp is considered numerically.

元の言語 英語 595-609 15 Journal of Mathematical Analysis and Applications 415 2 https://doi.org/10.1016/j.jmaa.2014.01.005 出版済み - 7 15 2014

### Fingerprint

Spectral Analysis
Harmonic Oscillator
Spectrum analysis
Lowest
Eigenvalue
Jacobi Matrix
Matrix Representation
Operator

### All Science Journal Classification (ASJC) codes

• Analysis
• Applied Mathematics

### これを引用

：: Journal of Mathematical Analysis and Applications, 巻 415, 番号 2, 15.07.2014, p. 595-609.

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AB - The lowest eigenvalue of non-commutative harmonic oscillators Q(α, β) (α>0, β>0, αβ>1) is studied. It is shown that Q(α, β) can be decomposed into four self-adjoint operators,Q(α,β)={N-ary circled plus operator}σ=±,p=1,2Qσp, and all the eigenvalues of each operator Qσp are simple. We show that the lowest eigenvalue of Q(α, β) is simple whenever α≠β. Furthermore a Jacobi matrix representation of Qσp is given and spectrum of Qσp is considered numerically.

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