Is Weak Pseudo-Hermiticity Weaker than Pseudo-Hermiticity?

Details Is Weak Pseudo-Hermiticity Weaker than Pseudo-Hermiticity? Is Weak Pseudo-Hermiticity Weaker than Pseudo-Hermiticity?

2006-05-12

arxiv.org/abs/quant-ph/0605110v3

J. Math. Phys. 47, 092101 (2006)

Physics

Quantum Physics

published version, 10 pages

Scientific paper

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.

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