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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
| 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 |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society |
| Descrizione fisica | 1 online resource (226 p.) |
| Disciplina | 512/.56 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Differential algebra
Darboux transformations Quantum theory - Mathematics |
| ISBN | 0-8218-8535-9 |
| Classificazione | 12H0533E3081Q6081Q8082B2333E99 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. |
| Record Nr. | UNINA-9910788636203321 |
| Providence, Rhode Island : , : American Mathematical Society | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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
| 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 |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society |
| Descrizione fisica | 1 online resource (226 p.) |
| Disciplina | 512/.56 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Differential algebra
Darboux transformations Quantum theory - Mathematics |
| ISBN | 0-8218-8535-9 |
| Classificazione | 12H0533E3081Q6081Q8082B2333E99 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. |
| Record Nr. | UNINA-9910822597303321 |
| Providence, Rhode Island : , : American Mathematical Society | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||