70881 20190709135515.0 doi 10.1088/1751-8121/aa739b sideral 99684 ART-2017-99684 eng (orcid)0000-0003-4480-6535 Cariñena, José F. Universidad de Zaragoza ABC of ladder operators for rationally extended quantum harmonic oscillator systems 2017 Access copy available to the general public Unrestricted The problem of construction of ladder operators for rationally extended quantum harmonic oscillator (REQHO) systems of a general form is investigated in the light of existence of different schemes of the Darboux-Crum-Krein-Adler transformations by which such systems can be generated from the quantum harmonic oscillator. Any REQHO system is characterized by the number of separated states in its spectrum, the number of valence bands in which the separated states are organized, and by the total number of the missing energy levels and their position. All these peculiarities of a REQHO system are shown to be detected and reflected by a trinity (A±, B±, C±) of the basic (primary) lowering and raising ladder operators related between themselves by certain algebraic identities with coefficients polynomially-dependent on the Hamiltonian. We show that all the secondary, higher-order ladder operators are obtainable by a composition of the basic ladder operators of the trinity which form the set of the spectrum-generating operators. Each trinity, in turn, can be constructed from the intertwining operators of the two complementary minimal schemes of the DarbouxCrumKreinAdler transformations. info:eu-repo/grantAgreement/ES/DGA/E24-1 info:eu-repo/grantAgreement/ES/MINECO/MTM2015-64166-C2-1 info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 1.963 2017 PHYSICS, MATHEMATICAL 13 / 55 = 0.236 2017 Q1 T1 PHYSICS, MULTIDISCIPLINARY 29 / 78 = 0.372 2017 Q2 T2 0.843 2017 Physics and Astronomy (miscellaneous) 2017 Q1 Modeling and Simulation 2017 Q1 Statistics and Probability 2017 Q2 Statistical and Nonlinear Physics 2017 Q2 Mathematical Physics 2017 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Plyushchay, Mikhail S. 2004 405 Universidad de Zaragoza Dpto. Física Teórica Área Física Teórica 50, 27 (2017), 275202 [30 pp.] Journal of Physics A-Mathematical and Theoretical Journal of Physics A-Mathematical and Theoretical 1751-8113 388830 http://zaguan.unizar.es/record/70881/files/texto_completo.pdf Postprint 91974 http://zaguan.unizar.es/record/70881/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:70881 articulos driver 2019-07-09-11:54:20 ARTICLE