Spectral Singularities Do Not Correspond to Bound States in the Continuum

TL;DR

This paper clarifies that spectral singularities are fundamentally different from bound states in the continuum, challenging previous claims and providing a clearer understanding of their distinct nature in quantum scattering theory.

Contribution

The paper demonstrates that spectral singularities do not correspond to bound states in the continuum, correcting a misconception in prior literature.

Findings

Spectral singularities are not equivalent to bound states in the continuum.

The distinction between spectral singularities and continuum bound states is clarified.

Previous claims linking these concepts are refuted.

Abstract

We show that, contrary to a claim made in arXiv:1011.0645, the von Neumann-Winger bound states that lie in the continuum of the scattering states are fundamentally different from Naimark's spectral singularities.