Ladder operators and rational extensions

TL;DR

This paper classifies ladder operators for rational extensions of the harmonic oscillator, framing them within a categorical structure, which simplifies the reproduction and extension of previous results.

Contribution

It introduces a categorical framework for rational extensions and their ladder operators, unifying and extending earlier findings.

Findings

Categorical structure REXT for rational extensions

Functor MD to REXT captures combinatorial data

Simplifies derivation of ladder operator properties

Abstract

This note presents the classification of ladder operators corresponding to the class of rational extensions of the harmonic oscillator. We show that it is natural to endow the class of rational extensions and the corresponding intertwining operators with the structure of a category REXT. The combinatorial data for this interpretation is realized as a functor MD $\to$ REXT, where MD refers to the set of Maya diagrams appropriately endowed with categorical structure. Our formalism allows us to easily reproduce and extend earlier results on ladder operators.