Darboux Transformations of Bispectral Quantum Integrable Systems
Abstract
We present an approach to higher dimensional Darboux transformations suitable for application to quantum integrable systems and based on the bispectral property of partial differential operators. Specifically, working with the algebrogeometric definition of quantum integrability, we utilize the bispectral duality of quantum Hamiltonian systems to construct nontrivial Darboux transformations between completely integrable quantum systems. As an application, we are able to construct new quantum integrable systems as the Darboux transforms of trivial examples (such as symmetric products of one dimensional systems) or by Darboux transformation of wellknown bispectral systems such as quantum CalogeroMoser.
 Publication:

arXiv eprints
 Pub Date:
 June 1998
 DOI:
 10.48550/arXiv.mathph/9806002
 arXiv:
 arXiv:mathph/9806002
 Bibcode:
 1998math.ph...6002H
 Keywords:

 Mathematical Physics;
 Mathematics  Commutative Algebra;
 Mathematics  Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Quantum Physics;
 Exactly Solvable and Integrable Systems;
 81S05 13N10 58G37 58F07 47F05 32C38
 EPrint:
 10 pages, no figures