On the pseudo-Hermitian nondiagonalizable Hamiltonians

Details On the pseudo-Hermitian nondiagonalizable Hamiltonians On the pseudo-Hermitian nondiagonalizable Hamiltonians

2002-11-25

arxiv.org/abs/quant-ph/0211161v1

Physics

Quantum Physics

22 pages

Scientific paper

We consider a class of (possibly nondiagonalizable) pseudo-Hermitian operators with discrete spectrum, showing that in no case (unless they are diagonalizable and have a real spectrum) they are Hermitian with respect to a semidefinite inner product, and that the pseudo-Hermiticity property is equivalent to the existence of an antilinear involutory symmetry. Moreover, we show that a typical degeneracy of the real eigenvalues (which reduces to the well known Kramers degeneracy in the Hermitian case) occurs whenever a fermionic (possibly nondiagonalizable) pseudo-Hermitian Hamiltonian admits an antilinear symmetry like the time-reversal operator $T$. Some consequences and applications are briefly discussed.

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