Ladder operators and rational extensions

2019/10/28 by David Gómez‐Ullate, Gomez-Ullate, David, Yves Grandati +5 · 1 citation
Computer Science · #13N10 #17B69 #81Q05 #Advanced Algebra and Logic #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1910.12648

openalex publication_date 2019/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 → 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.

Cited by

• Extended Coherent States

Related

• Equivalent non-rational extensions of the harmonic oscillator, their ladder operators and coherent states
• Ladder operators with no vacuum, their coherent states, and an application to graphene
• Coding with ladders a well-ordering of the reals
• Some classes of finite-dimensional ladder operators
• Constructing Coherent States for the Rational Extensions of the Harmonic Oscillator Potential