Epsilon coherent states with polyanalytic coefficients for the harmonic oscillator

TL;DR

This paper introduces a novel class of epsilon-coherent states for the harmonic oscillator using polyanalytic functions, which solve the identity in the Hilbert space and exhibit thermal stability, with explicit wavefunctions and a Bargmann-type transform.

Contribution

The paper develops a new family of coherent states based on polyanalytic functions, extending the canonical states with a parameter-dependent construction and stability properties.

Findings

States solve the identity in the Hilbert space as epsilon approaches zero

Wavefunctions are obtained in a closed form

Associated Bargmann-type transform is discussed

Abstract

We construct a new class of coherent states indexed by points z of the complex plane and depending on two positive parameters m and epsilon by replacing the coefficients of the canonical coherent states by polyanalytic functions. These states solve the identity of the states Hilbert space of the harmonic oscillator at the limit epsilon goes to zero and obey a thermal stability property. Their wavefunctions are obtained in a closed form and their associated Bargmann-type transform is also discussed.