LEADER 04459nam 2200577 450 001 9910788636203321 005 20220823074619.0 010 $a0-8218-8535-9 035 $a(CKB)3240000000070086 035 $a(EBL)3113337 035 $a(SSID)ssj0000601382 035 $a(PQKBManifestationID)11361987 035 $a(PQKBTitleCode)TC0000601382 035 $a(PQKBWorkID)10566369 035 $a(PQKB)10960870 035 $a(MiAaPQ)EBC3113337 035 $a(RPAM)17113804 035 $a(PPN)197102069 035 $a(EXLCZ)993240000000070086 100 $a20120110h20122012 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aAlgebraic aspects of Darboux transformations, quantum integrable systems and supersymmetric quantum mechanics $eJairo Charris Seminar 2010, Universidad Sergio Arboleda, Santa Marta, Colombia /$fPrimitivo B. Acosta-Huma?nez [and three others], editors 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society ;$a[Madrid] :$cInstituto de Matematicas y sus Aplicaciones,$d[2012] 210 4$dİ2012 215 $a1 online resource (226 p.) 225 1 $aContemporary mathematics,$v563$x0271-4132 300 $aDescription based upon print version of record. 311 $a0-8218-7584-1 320 $aIncludes bibliographical references. 327 $aPreface -- 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 I??-functons -- 6. Integration as a linearly exponential I??-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. 410 0$aContemporary mathematics (American Mathematical Society).$v563$x0271-4132 606 $aDifferential algebra$vCongresses 606 $aDarboux transformations$vCongresses 606 $aQuantum theory$xMathematics$vCongresses 615 0$aDifferential algebra 615 0$aDarboux transformations 615 0$aQuantum theory$xMathematics 676 $a512/.56 686 $a12H05$a33E30$a81Q60$a81Q80$a82B23$a33E99$2msc 702 $aAcosta Humanez$b Primitivo B. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788636203321 996 $aAlgebraic aspects of Darboux transformations, quantum integrable systems, and supersymmetric quantum mechanics$9241049 997 $aUNINA