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Journal | Journal of Physics A: Mathematical and General |
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Date | Published - 11 Aug 2006 |

Issue number | 32 |

Volume | 39 |

Number of pages | 8 |

Pages (from-to) | 10239-10246 |

Original language | English |

A fundamental problem in the theory of PT-invariant quantum systems is to determine whether a given system 'respects' this symmetry or not. If not, the system usually develops non-real eigenvalues. It is shown in this contribution how to algorithmically detect the existence of complex eigenvalues for a given PT-symmetric matrix. The procedure uses classical results from stability theory which qualitatively locate the zeros of real polynomials in the complex plane. The interest and value of the present approach lies in the fact that it avoids diagonalization of the Hamiltonian at hand.

© 2006 IOP Publishing Ltd. This is an author produced version of a paper published in Journal of Physics A: Mathematical and General.

- QUANTUM-MECHANICS, SQUARE-WELL, DIAGONALIZABILITY, SYSTEMS

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