Generalized PT symmetry and real spectra

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Published 26 July 2002 • Published under licence by IOP Publishing Ltd
, , Citation Carl M Bender et al 2002 J. Phys. A: Math. Gen. 35 L467 DOI 10.1088/0305-4470/35/31/101

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1 Department of Physics, Washington University, St Louis, MO 63130, USA

2 H H Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, UK

Dates

  1. Received 8 May 2002
  2. Published

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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 A2k = 1 with k odd. The argument is illustrated by a 2 × 2 matrix Hamiltonian, and two examples of the generalization are given.

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