Spectral Singularities of a General Point Interaction

TL;DR

This paper investigates spectral singularities and bound states of complex point interactions, analyzing symmetry cases and the coalescence phenomena to deepen understanding of their spectral properties.

Contribution

It provides a comprehensive analysis of spectral singularities, bound states, and symmetry cases for general complex point interactions, including coalescence phenomena.

Findings

Identification of spectral singularities and bound states

Analysis of P-, T-, and PT-symmetric cases

Insights into coalescence of spectral singularities and bound states

Abstract

We study the problem of locating spectral singularities of a general complex point interaction with a support at a single point. We also determine the bound states, examine the special cases where the point interaction is P-, T-, and PT-symmetric, and explore the issue of the coalescence of spectral singularities and bound states.