### Abstract

Using representation-theoretic methods, we determine the spectrum of the 2 × 2 system Q(x, D_{x}) = A(-∂_{x}/^{2}/2 + x^{2}/2) + B(x∂_{x} + 1/2), x ∈ R, with A,B ∈ Mat_{2}(R) constant matrices such that A = ^{t}A > 0 (or < 0), B = -^{t}B ≠ 0, and the Hermitian matrix A + iB positive (or negative) definite. We also give results that generalize (in a possible direction) the main construction.

Original language | English |
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Pages (from-to) | 26-30 |

Number of pages | 5 |

Journal | Proceedings of the National Academy of Sciences of the United States of America |

Volume | 98 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2 2001 |

### All Science Journal Classification (ASJC) codes

- General

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## Cite this

Parmeggiani, A., & Wakayama, M. (2001). Oscillator representations and systems of ordinary differential equations.

*Proceedings of the National Academy of Sciences of the United States of America*,*98*(1), 26-30. https://doi.org/10.1073/pnas.98.1.26