Coherent states associated to the wavefunctions and the spectrum of the isotonic oscillator

TL;DR

This paper introduces new classes of coherent states for the isotonic oscillator, utilizing confluent hypergeometric functions, and identifies their stability and relation to Mittag-Leffler coherent states.

Contribution

The work constructs novel coherent states for the isotonic oscillator using hypergeometric functions and establishes their temporal stability and connection to Mittag-Leffler states.

Findings

Coherent states are formulated using confluent hypergeometric functions.

The states are shown to be temporally stable for the isotonic oscillator.

These states are identified as a special case of Mittag-Leffler coherent states.

Abstract

Classes of coherent states are presented by replacing the labeling parameter $z$ of Klauder-Perelomov type coherent states by confluent hypergeometric functions with specific parameters. Temporally stable coherent states for the isotonic oscillator Hamiltonian are presented and these states are identified as a particular case of the so-called Mittag-Leffler coherent states.