Point Interactions: PT-Hermiticity and Reality of the Spectrum

Details Point Interactions: PT-Hermiticity and Reality of the Spectrum Point Interactions: PT-Hermiticity and Reality of the Spectrum

2002-06-18

arxiv.org/abs/quant-ph/0206112v1

Lett. Math. Phys. 59, 2002(227-242)

Physics

Quantum Physics

17 pages

Scientific paper

General point interactions for the second derivative operator in one dimension are studied. In particular, ${\mathcal P \mathcal T}$-self-adjoint point interactions with the support at the origin and at points $\pm l$ are considered. The spectrum of such non-Hermitian operators is investigated and conditions when the spectrum is pure real are presented. The results are compared with those for standard self-adjoint point interactions.

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