A generating function for Hermite polynomials in connection with Euclidean Landau levels

TL;DR

This paper derives a generating function for Hermite polynomials by linking two coherent state representations associated with Euclidean Landau levels, combining series expansion and group theory methods.

Contribution

It introduces a novel generating function for Hermite polynomials through a comparison of two coherent state formulations related to Landau levels.

Findings

Derived a new generating function for Hermite polynomials.

Connected group representation theory with coherent states for Landau levels.

Bridged two different expressions of coherent states in the context of Hermite polynomials.

Abstract

We have formulated a generating function for the Hermite polynomials by comparing two expressions of the same coherent states attached to planar Landau levels. A first expression is obtained by generalizing the canonical coherent states when written as series expansion in the basis of number states. While the second expression is established by following a construction based on group representation theory.