Ladder operators and rational extensions
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.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 arXiv:
 arXiv:1910.12648
 Bibcode:
 2019arXiv191012648G
 Keywords:

 Mathematical Physics;
 Quantum Physics;
 13N10;
 17B69;
 81Q05
 EPrint:
 8 pages, 1 figure