A Unified Theory of Quasibound States

TL;DR

This paper introduces a comprehensive formalism that unifies the treatment of quasibound states and quantum resonances, providing clear distinctions and extending applicability to various spectra.

Contribution

It develops a unified theoretical framework for quasibound states and resonances, clarifying distinctions and extending to degenerate and continuous spectra.

Findings

Unified formalism for quasibound states and resonances

Clear criteria to distinguish quasibound states from continuum

Application to multiple spectra including degenerate levels

Abstract

We have developed a formalism that includes both quasibound states with real energies and quantum resonances within the same theoretical framework, and that admits a clean and unambiguous distinction between these states and the states of the embedding continuum. States described broadly as 'quasibound' are defined as having a connectedness (in the mathematical sense) to true bound states through the growth of some parameter. The approach taken here builds on our earlier work by clarifying several crucial points and extending the formalism to encompass a variety of continuous spectra, including those with degenerate energy levels. The result is a comprehensive framework for the study of quasibound states. The theory is illustrated by examining several cases pertinent to applications widely discussed in the literature.