Constructing Coherent States for the Rational Extensions of the Harmonic Oscillator Potential

TL;DR

This paper develops a method to construct coherent states for rational extensions of the harmonic oscillator using algebraic formalism, providing exact solutions to the Schrödinger equation.

Contribution

It introduces a novel algebraic approach with Maya diagrams and ladder operators to build coherent states for extended harmonic oscillators.

Findings

Constructed coherent states for rational harmonic oscillator extensions.

Provided exact time-dependent solutions to the Schrödinger equation.

Established a joint eigenfunction framework for annihilating operators.

Abstract

Using the formalism of Maya diagrams and ladder operators, we describe the algebra of annihilating operators for the class of rational extensions of the harmonic oscillators. This allows us to construct the corresponding coherent state in the sense of Barut and Girardello. The resulting time-dependent function is an exact solution of the time-dependent Schrodinger equation and a joint eigenfunction of the algebra of annihilators.