Scattering states and bound states of exponential potentials

TL;DR

This paper investigates the connection between scattering and bound states in exponential potentials with non-analytic segments, clarifying the nature of special scattering states and extending analysis to power potentials like $x^3$.

Contribution

It provides a detailed analysis of scattering and bound states in exponential potentials with non-analytic segments, clarifying the status of special scattering states and extending the approach to power potentials.

Findings

Clarified the relationship between scattering and bound states in exponential potentials.

Analyzed the special scattering states identified in previous work.

Extended the analysis to non-analytic segments of power potentials such as $x^3$.

Abstract

We explore the relationships between scattering states and bound states of different non-analytic segments (depending on $|x|$) of the exponential potential, and elucidate the status of the special scattering states found in an earlier publication by Ahmed et al. A similar analysis can be made of non-analytic segments of power potentials such as $x^3$.