arXiv:0710.4879 · Journal of Physics A Mathematical and Theoretical

\mathcal{Q}\mathcal{T} -symmetry and weak pseudo-hermiticity

Ali Mostafazadeh

Published Jan 23, 2008• 20 citations

Abstract

For an invertible (bounded) linear operator acting in a Hilbert space , we consider the consequences of the -symmetry of a non-hermitian Hamiltonian where is the time-reversal operator. If H is symmetric in the sense that , then -symmetry is equivalent to -weak-pseudo-hermiticity. But in general this equivalence does not hold. We show this using some specific examples. Among these is a large class of non- -symmetric Hamiltonians that share the spectral properties of -symmetric Hamiltonians.

DOI: 10.1088/1751-8113/41/5/055304

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