### Abstract

The fact that eigenvalues of PT-symmetric Hamiltonians H can be real for some values of a parameter and complex for others is explained by showing that the matrix elements of H, and hence the secular equation, are real, not only for PT but also for any antiunitary operator A satisfying A^{2k} = 1 with k odd. The argument is illustrated by a 2 × 2 matrix Hamiltonian, and two examples of the generalization are given.

Original language | English |
---|---|

Journal | Journal of Physics A: Mathematical and General |

Volume | 35 |

Issue number | 31 |

DOIs | |

Publication status | Published - Aug 9 2002 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*35*(31). https://doi.org/10.1088/0305-4470/35/31/101

**Generalized PT symmetry and real spectra.** / Bender, Carl M.; Berry, M. V.; Mandilara, Aikaterini.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 35, no. 31. https://doi.org/10.1088/0305-4470/35/31/101

}

TY - JOUR

T1 - Generalized PT symmetry and real spectra

AU - Bender, Carl M.

AU - Berry, M. V.

AU - Mandilara, Aikaterini

PY - 2002/8/9

Y1 - 2002/8/9

N2 - The fact that eigenvalues of PT-symmetric Hamiltonians H can be real for some values of a parameter and complex for others is explained by showing that the matrix elements of H, and hence the secular equation, are real, not only for PT but also for any antiunitary operator A satisfying A2k = 1 with k odd. The argument is illustrated by a 2 × 2 matrix Hamiltonian, and two examples of the generalization are given.

AB - The fact that eigenvalues of PT-symmetric Hamiltonians H can be real for some values of a parameter and complex for others is explained by showing that the matrix elements of H, and hence the secular equation, are real, not only for PT but also for any antiunitary operator A satisfying A2k = 1 with k odd. The argument is illustrated by a 2 × 2 matrix Hamiltonian, and two examples of the generalization are given.

UR - http://www.scopus.com/inward/record.url?scp=0037047597&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037047597&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/35/31/101

DO - 10.1088/0305-4470/35/31/101

M3 - Article

AN - SCOPUS:0037047597

VL - 35

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 31

ER -