Non Hermitian Operators with Real Spectrum in Quantum Mechanics

Details Non Hermitian Operators with Real Spectrum in Quantum Mechanics Non Hermitian Operators with Real Spectrum in Quantum Mechanics

2009-09-16

arxiv.org/abs/0909.3054v4

Physics

Quantum Physics

Scientific paper

Examples are given of non-Hermitian Hamiltonian operators which have a real spectrum. Some of the investigated operators are expressed in terms of the generators of the Weil-Heisenberg algebra. It is argued that the existence of an involutive operator $\hat J$ which renders the Hamiltonian $\hat J$-Hermitian leads to the unambiguous definition of an associated positive definite norm allowing for the standard probabilistic interpretation of quantum mechanics. Non-Hermitian extensions of the Poeschl-Teller Hamiltonian are also considered. Hermitian counterparts obtained by similarity transformations are constructed.

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