Some physical applications of generalized Lambert functions

TL;DR

This paper reviews various physical applications of the generalized Lambert function, highlighting its role in quantum physics, relativity, differential equations, and fluid dynamics, and clarifies its relation to the inverse Langevin function.

Contribution

It provides a comprehensive overview of the applications of the recently defined generalized Lambert function in multiple physical contexts.

Findings

Application to eigenstate anomaly of H2+ ion

Use in stability analysis of delay differential equations

Connection to inverse Langevin function

Abstract

In this paper we review the physical applications of the generalized Lambert function recently defined by the first author. Among these applications we mention the eigenstate anomaly of the $H_2^+$ ion, the two dimensional two-body problem in general relativity, the stability analysis of delay differential equations and water-wave applications. We also point out that the inverse Langevin function is nothing else but a specially parametrized generalized Lambert function.