04459nam 2200577 450 991082259730332120220823074619.00-8218-8535-9(CKB)3240000000070086(EBL)3113337(SSID)ssj0000601382(PQKBManifestationID)11361987(PQKBTitleCode)TC0000601382(PQKBWorkID)10566369(PQKB)10960870(MiAaPQ)EBC3113337(RPAM)17113804(PPN)197102069(EXLCZ)99324000000007008620120110h20122012 uy| 0engur|n|---|||||txtccrAlgebraic aspects of Darboux transformations, quantum integrable systems and supersymmetric quantum mechanics Jairo Charris Seminar 2010, Universidad Sergio Arboleda, Santa Marta, Colombia /Primitivo B. Acosta-Humánez [and three others], editorsProvidence, Rhode Island :American Mathematical Society ;[Madrid] :Instituto de Matematicas y sus Aplicaciones,[2012]©20121 online resource (226 p.)Contemporary mathematics,5630271-4132Description based upon print version of record.0-8218-7584-1 Includes bibliographical references.Preface -- Spectral/quadrature duality: Picard-Vessiot theory and finite-gap potentials -- 1. Introduction -- 2. Background -- 3. Integrability of equation (1) by Picard-Vessiot -- 4. Spectral/quadrature duality. An integration procedure -- 5. The Î?-functons -- 6. Integration as a linearly exponential Î?-extension -- 7. Integrability and differential closedness -- 8. Definition of through Liouvillian extension -- 9. Non-finite-gap integrable counterexamples -- 10. Concluding remarks -- References -- Darboux transformation, exceptional orthogonal polynomials and information theoretic measures of uncertainty -- 1. Introduction -- 2. A brief outline of supersymmetric quantum mechanics -- 3. EOP's associated with broken supersymmetry -- 4. Relation with higher order Darboux transformation -- 5. Information-theoretic lengths for the partner potential of linear harmonic oscillator via supersymmetry -- 6. Moment of the quantum mechanical states associated with the partner of harmonic oscillator via supersymmetry -- 7. Discussion: -- References -- On orthogonal polynomials spanning a non-standard flag -- 1. Introduction -- 2. Preliminaries -- 3. Codimension 1 flags -- 4. Higher codimension flags -- Acknowledgements -- References -- On the Supersymmetric Spectra of two Planar Integrable Quantum Systems -- 1. Introduction -- 2. =2 supersymmetric planar quantum systems -- 3. The planar quantum Kepler/Coulomb problem and supersymmetry -- 4. The planar quantum Euler/Coulomb problem and supersymmetry -- 5. Two center collapse in one center -- 6. Further comments -- Acknowledgements -- References -- Solvable rational extension of translationally shape invariant potentials -- Introduction -- 1. Solvable rational extensions of the harmonic oscillator -- 2. Second category potentials -- 3. Conclusion -- Acknowledgments -- References -- The pentagram map: geometry, algebra, integrability -- 1. Introduction: The pentagram map -- 2. Complete integrability of the pentagram map on the space _{ } -- 3. Relation to the Boussinesq equation -- 4. The space _{ } and 2-frieze patterns -- Acknowledgments -- References -- Jet Bundles, symmetries, Darboux transforms -- Elliptic beta integrals and solvable models of statistical mechanics.Contemporary mathematics (American Mathematical Society).5630271-4132Differential algebraCongressesDarboux transformationsCongressesQuantum theoryMathematicsCongressesDifferential algebraDarboux transformationsQuantum theoryMathematics512/.5612H0533E3081Q6081Q8082B2333E99mscAcosta Humanez Primitivo B.MiAaPQMiAaPQMiAaPQBOOK9910822597303321Algebraic aspects of Darboux transformations, quantum integrable systems, and supersymmetric quantum mechanics241049UNINA