Banach Journal of Mathematical Analysis

Non-self-adjoint Schrödinger operators with nonlocal one-point interactions

Sergii Kuzhel and Miloslav Znojil

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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.

Article information

Banach J. Math. Anal., Volume 11, Number 4 (2017), 923-944.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B25: Symmetric and selfadjoint operators (unbounded)
Secondary: 35P05: General topics in linear spectral theory

1-dimensional Schrödinger operator nonlocal one-point interactions boundary triplet


Kuzhel, Sergii; Znojil, Miloslav. Non-self-adjoint Schrödinger operators with nonlocal one-point interactions. Banach J. Math. Anal. 11 (2017), no. 4, 923--944. doi:10.1215/17358787-2017-0032.

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