Algebraic 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], editors

• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society; [Madrid] : , : Instituto de Matematicas y sus Aplicaciones, , [2012]; ©2012
• Descrizione fisica: 1 online resource (226 p.)
• Disciplina: 512/.56
• Soggetto topico: Differential algebra; Darboux transformations; Quantum theory - Mathematics
• Classificazione: 12H0533E3081Q6081Q8082B2333E99
• Persona (resp. second.): Acosta HumanezPrimitivo B.
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: 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.
• Titolo autorizzato: Algebraic aspects of Darboux transformations, quantum integrable systems, and supersymmetric quantum mechanics
• ISBN: 0-8218-8535-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910788636203321
• Lo trovi qui: Univ. Federico II
• Serie: Contemporary mathematics (American Mathematical Society). ; 563 . 0271-4132