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October 2017 Non-self-adjoint Schrödinger operators with nonlocal one-point interactions
Sergii Kuzhel, Miloslav Znojil
Banach J. Math. Anal. 11(4): 923-944 (October 2017). DOI: 10.1215/17358787-2017-0032


We generalize and study, within the framework of quantum mechanics and working with 1-dimensional, manifestly non-Hermitian Hamiltonians H=d2/dx2+V, the traditional class of exactly solvable models with local point interactions V=V(x). We discuss the consequences of the use of nonlocal point interactions such that (Vf)(x)=K(x,s)f(s)ds by means of the suitably adapted formalism of boundary triplets.


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Sergii Kuzhel. Miloslav Znojil. "Non-self-adjoint Schrödinger operators with nonlocal one-point interactions." Banach J. Math. Anal. 11 (4) 923 - 944, October 2017.


Received: 4 September 2016; Accepted: 12 January 2017; Published: October 2017
First available in Project Euclid: 11 September 2017

zbMATH: 06841261
MathSciNet: MR3708536
Digital Object Identifier: 10.1215/17358787-2017-0032

Primary: 47B25
Secondary: 35P05

Keywords: 1-dimensional Schrödinger operator , boundary triplet , nonlocal one-point interactions

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 4 • October 2017
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