Pseudo-hermiticity of Hamiltonians under gaugelike transformation. Real spectrum of nonHermitian Hamiltonians

Ahmed, Z.

doi:10.1016/S0375-9601(02)00124-X

Pseudo-hermiticity of Hamiltonians under gaugelike transformation. Real spectrum of nonHermitian Hamiltonians

Z. Ahmed
(
- Bhabha Atomic Res. Ctr.
)

Mar, 2002

5 pages

Published in:

Phys.Lett.A 294 (2002) 287-291

DOI:

10.1016/S0375-9601(02)00124-X

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Abstract: (Elsevier)

We report that it is the pseudo-Hermiticity of Hamiltonians under the gauge-like transformation that underlies the reality of the spectrum and orthogonality of states for the non-Hermitian Hamiltonians type H β =[ p + iβν ( x )] 2 /2 m + V ( x ), which could be both PT -symmetric and non- PT -symmetric. Notably, the eigenstates of H β , when it is PT -symmetric, are real and do not satisfy the PT -orthogonality condition.

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