arXiv:quant-ph/0605110 · Journal of Mathematical Physics

Is weak pseudo-Hermiticity weaker than pseudo-Hermiticity?

Alí Mostafazadeh

Published Sep 1, 2006• 14 citations

Abstract

For a weakly pseudo-Hermitian linear operator, we give a spectral condition that ensures its pseudo-Hermiticity. This condition is always satisfied whenever the operator acts in a finite-dimensional Hilbert space. Hence weak pseudo-Hermiticity and pseudo-Hermiticity are equivalent in finite-dimensions. This equivalence extends to a much larger class of operators. Quantum systems whose Hamiltonian is selected from among these operators correspond to pseudo-Hermitian quantum systems possessing certain symmetries.

DOI: 10.1063/1.2338144

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