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Generalized PT symmetry and real spectra

2002; Institute of Physics; Volume: 35; Issue: 31 Linguagem: Inglês

10.1088/0305-4470/35/31/101

1361-6447

Carl M. Bender, Marsha Berry, Aikaterini Mandilara,

Quantum chaos and dynamical systems

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.