Quantum solvable models with nonlocal one point interactions

TL;DR

This paper generalizes exactly solvable quantum models by introducing nonlocal one-point interactions, expanding the class of solvable Hamiltonians beyond traditional local point interactions using boundary triplet formalism.

Contribution

It introduces a framework for exactly solvable quantum models with nonlocal point interactions, extending the traditional local interaction models.

Findings

Development of a formalism for nonlocal point interactions

Extension of solvable models to nonlocal interactions

Analysis of the implications of nonlocal interactions in quantum mechanics

Abstract

Within the framework of quantum mechanics working with one-dimensional, manifestly non-Hermitian Hamiltonians $H=T+V$ the traditional class of the exactly solvable models with local point interactions $V=V(x)$ is generalized. The consequences of the use of the nonlocal point interactions such that $(V f)(x) = \int K(x,s) f(s) ds$ are discussed using the suitably adapted formalism of boundary triplets.