Ladder operators' normal ordering problem for quantum-deformed systems and the (q, p)-generalization of the Stirling and Bell numbers

• Published in: Journal of physics. A, Mathematical and theoretical Vol. 43; no. 27; p. 275307
• Main Authors: Aleixo, A N F, Balantekin, A B
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 09.07.2010; IOP
• Subjects: Bells; Exact sciences and technology; Formalism; Integers; Ladders; Mathematical analysis; Operators; Order disorder; Physics; Strings; Operator; Quantum system; Deformation; Morse potential; Invarying system
• ISSN: 1751-8121; 1751-8113; 1751-8121
• DOI: 10.1088/1751-8113/43/27/275307

We resolve the ladder operators normal ordering problem for strings in the form for (q, p)-deformed supersymmetric and shape-invariant potential systems, where n is a positive integer. We provide exact and explicit expressions for their normal form , where in all are at the right-hand side, and find that the solution involves expansion-coefficients sequence which corresponds to the generalization, for any (q, p)-deformed shape-invariant potential system, of the classical Stirling and Bell numbers. We show that these numbers are given for expressions depending on parameters related to the forms of supersymmetric partner potentials and the system quantum deformation. We apply the general formalism to Poschl--Teller, Morse and Scarf potential systems.