Is Weak Pseudo-Hermiticity Weaker than Pseudo-Hermiticity?

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.

published version, 10 pages

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• A Novel SUSY Energy Bound States Treatment of the Klein-Gordon Equation with PT-Supersymmetric and q-Deformed Hulthen Potential
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