# Study of superradiance in the Lambert-W potential barrier

## TL;DR

This paper investigates superradiance phenomena in a novel Lambert-W potential barrier by calculating transmission and reflection coefficients, comparing results with known potentials, and solving the Klein-Gordon equation using Heun Confluent functions.

## Contribution

It introduces a new Lambert-W potential barrier exhibiting superradiance and provides analytical solutions using Heun Confluent functions, expanding understanding of wave behavior in such potentials.

## Key findings

- Superradiance occurs when reflection coefficient exceeds one.
- Transmission and reflection coefficients are computed for different regions.
- Analytical solutions are obtained using Heun Confluent functions.

## Abstract

We present a new potential barrier that presents the phenomenon of superradiance when the reflection coefficient $R$ is greater than one. We calculated the transmission and reflection coefficients for three different regions. The results are compared with those obtained for the hyperbolic tangent potential barrier and the step potential barrier. We also present the solution of the Klein-Gordon equation with the Lambert-W potential barrier in terms of the Heun Confluent functions.