Quantum, classical symmetries and action-angle variables by factorization of superintegrable systems

The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this procedure to the harmonic oscillator and Kepler-Coulomb systems to show the differences with other more standard approaches. We have described in detail the basic ingredients to make explicit the parallelism of classical and quantum treatments. One of the most interesting results is the finding of action-angle variables as a natural component of the classical sysmmetries within this formalism.Comment: 21 pages, 3 figure

Unusual isospectral factorizations of shape invariant Hamiltonians with Scarf II potential

In this paper, we search the factorizations of the shape invariant Hamiltonians with Scarf II potential. We find two classes; one of them is the standard real factorization which leads us to a real hierarchy of potentials and their energy levels; the other one is complex and it leads us naturally to a hierarchy of complex Hamiltonians. We will show some properties of these complex Hamiltonians: they are not parity-time (or PT) symmetric, but their spectrum is real and isospectral to the Scarf II real Hamiltonian hierarchy. The algebras for real and complex shift operators (also called potential algebras) are computed; they consist of $su(1,1)$ for each of them and the total potential algebra including both hierarchies is the direct sum $su(1,1)\oplus su(1,1)$.Comment: 13 pages, 5 figure

SUSY partners and SS-matrix poles of the one dimensional Rosen-Morse II Hamiltonian

Among the list of one dimensional solvable Hamiltonians, we find the Hamiltonian with the Rosen-Morse II potential. The first objective is to analyze the scattering matrix corresponding to this potential. We show that it includes a series of poles corresponding to the types of redundant poles or anti-bound poles. In some cases, there are even bound states and this depends on the values of given parameters. Then, we perform different supersymmetric transformations on the original Hamiltonian using the ground state (for those situations where there are bound states) wave functions, or other wave functions that comes from anti-bound states or redundant states. We study the properties of these transformations.Comment: 20 pages, 6 figure

Factorizations of one dimensional classical systems

A class of one dimensional classical systems is characterized from an algebraic point of view. The Hamiltonians of these systems are factorized in terms of two functions that together with the Hamiltonian itself close a Poisson algebra. These two functions lead directly to two time-dependent integrals of motion from which the phase motions are derived algebraically. The systems so obtained constitute the classical analogues of the well known factorizable one dimensional quantum mechanical systems.Comment: 19 pages, 7 figure

Towards a standardized program of transitional care for adolescents with juvenile idiopathic arthritis for Turkey: a national survey study

Background: Juvenile idiopathic arthritis (JIA) is a prevalent childhood chronic arthritis, often persisting into adulthood. Effective transitional care becomes crucial as these patients transition from pediatric to adult healthcare systems. Despite the concept of transitional care being recognized, its real-world implementation remains inadequately explored. This study aims to evaluate the thoughts and practices of healthcare providers regarding transitional care for JIA patients. Methods: A cross-sectional survey was conducted among pediatric and adult rheumatologists in Turkey. Based on the American Academy of Pediatrics’ six core elements of transitional care, the survey included 86 questions. The respondents’ demographic data, attitudes towards transitional care, and practical implementation were assessed. Results: The survey included 48 rheumatologists, with 43.7% having a transition clinic. The main barriers to establishing transition programs were the absence of adult rheumatologists, lack of time, and financial constraints. Only 23.8% had a multidisciplinary team for transition care. Participants agreed on the importance of coordination and cooperation between pediatric and adult healthcare services. The timing of the transition process varied, with no consensus on when to initiate or complete it. Participants advocated for validated questionnaires adapted to local conditions to assess transition readiness. Conclusions: The study sheds light on the challenges and perspectives surrounding transitional care for JIA patients in Turkey. Despite recognized needs and intentions, practical implementation remains limited due to various barriers. Cultural factors and resource constraints affect the transition process. While acknowledging the existing shortcomings, the research serves as a ground for further efforts to improve transitional care and ensure better outcomes for JIA patients transitioning into adulthood