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Point Interactions: PT-Hermiticity and Reality of the Spectrum

S. Albeverio·S. M. Fei·P. Kurasov
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Abstract

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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S. Albeverio, S. M. Fei, P. Kurasov. 2002-06-18. Point Interactions: PT-Hermiticity and Reality of the Spectrum. https://arxiv.org/abs/quant-ph/0206112

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