Darboux Transformations of Bispectral Quantum Integrable Systems

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dc.creatorHorozov, Emil
dc.creatorKasman, Alex
dc.date1998-06-05
dc.date.accessioned2026-07-07T04:32:25Z
dc.date.available2026-07-07T04:32:25Z
dc.descriptionWe 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 algebro-geometric definition of quantum integrability, we utilize the bispectral duality of quantum Hamiltonian systems to construct non-trivial 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 well-known bispectral systems such as quantum Calogero-Moser.
dc.description10 pages, no figures
dc.identifierhttps://arxiv.org/abs/math-ph/9806002
dc.identifierhttp://arxiv.org/abs/math-ph/9806002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58183
dc.subjectMathematical Physics
dc.subjectCommutative Algebra
dc.subjectExactly Solvable and Integrable Systems
dc.subjectQuantum Physics
dc.subject81S05 13N10 58G37 58F07 47F05 32C38
dc.titleDarboux Transformations of Bispectral Quantum Integrable Systems
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