Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics
About this Volume
Edited by: Primitivo B. Acosta-Humánez, Universidad del Norte, Barranquilla, Colombia, Federico Finkel, Universidad Complutense de Madrid, Madrid, Spain, Niky Kamran, McGill University, Montreal, Quebec, Canada and Peter J. Olver, University of Minnesota, Minneapolis, MN
2012: Volume: 563
ISBNs: 978-0-8218-7584-1 (print); 978-0-8218-8535-2 (online)
This volume represents the 2010 Jairo Charris Seminar in Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, which was held at the Universidad Sergio Arboleda in Santa Marta, Colombia.
The papers cover the fields of Supersymmetric Quantum Mechanics and Quantum Integrable Systems, from an algebraic point of view. Some results presented in this volume correspond to the analysis of Darboux Transformations in higher order as well as some exceptional orthogonal polynomials.
The reader will find an interesting Galois approach to study finite gap potentials.
Graduate students and research mathematicians interested in algebraic aspects of Supersymmetric Quantum Mechanics and Integrable systems.
Table of Contents
- Yurii V. Brezhnev – Spectral/quadrature duality: Picard–Vessiot theory and finite-gap potentials
- D. Dutta and P. Roy – Darboux transformation, exceptional orthogonal polynomials and information theoretic measures of uncertainty
- David Gómez-Ullate, Niky Kamran and Robert Milson – On orthogonal polynomials spanning a non-standard flag
- M. A. Gonzalez Leon, J. Mateos Guilarte, M. J. Senosiain and M. de la Torre Mayado – On the Supersymmetric Spectra of two Planar Integrable Quantum Systems
- Yves Grandati and Alain Bérard – Solvable rational extension of translationally shape invariant potentials
- Valentin Ovsienko – The pentagram map: geometry, algebra, integrability
- Enrique G. Reyes – Jet Bundles, symmetries, Darboux transforms
- Axel Schulze-Halberg – Explicit higher-dimensional Darboux transformations for the time-dependent Schrödinger equation
- V. P. Spiridonov – Elliptic beta integrals and solvable models of statistical mechanics