04526nam 2200613 450 991048011670332120180613001242.00-8218-8535-9(CKB)3240000000070086(EBL)3113337(SSID)ssj0000601382(PQKBManifestationID)11361987(PQKBTitleCode)TC0000601382(PQKBWorkID)10566369(PQKB)10960870(MiAaPQ)EBC3113337(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 ;volume 563Description based upon print version of record.0-8218-7584-1 Includes bibliographical references.""Preface""; ""Spectral/quadrature duality: Picardâ€?Vessiot theory and finite-gap potentials""; ""1. Introduction""; ""2. Background""; ""3. Integrability of equation (1) by Picardâ€?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. EOPâ€?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) ;v. 563.Differential algebraCongressesDarboux transformationsCongressesQuantum theoryMathematicsCongressesElectronic books.Differential algebraDarboux transformationsQuantum theoryMathematics512/.56Acosta Humanez Primitivo B.MiAaPQMiAaPQMiAaPQBOOK9910480116703321Algebraic aspects of Darboux transformations, quantum integrable systems, and supersymmetric quantum mechanics241049UNINA