## Infinite order symmetries for two-dimensional separable Schrödinger equations

dc.contributor.author | Kalnins, Ernie G. | |

dc.contributor.author | Miller, W., Jr. | |

dc.contributor.author | Pogosyan, G.S. | |

dc.coverage.spatial | Conference held at Kyiv, Ukraine | en_NZ |

dc.date.accessioned | 2009-01-11T20:13:22Z | |

dc.date.available | 2009-01-11T20:13:22Z | |

dc.date.issued | 2004 | |

dc.identifier.citation | Kalnins, E.G., Miller, W., Jr. & Pogosyan, G.S.(2004). Infinite order symmetries for two-dimensional separable Schrödinger equations. In Proceedings of Institute of Mathematics of NAS of Ukraine, 50(1), 184-195. | en |

dc.identifier.uri | https://hdl.handle.net/10289/1763 | |

dc.description.abstract | Consider a non-relativistic Hamiltonian operator H in 2 dimensions consisting of a kinetic energy term plus a potential. We show that if the associated Schrödinger eigenvalue equation admits an orthogonal separation of variables, there is a calculus to describe the (in general) infinite-order differential operator symmetries of the Schrödinger equation. The calculus is formal but can be made rigorous when all functions in the eigenvaue equation are analytic. The infinite-order calculus exhibits structure that is not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. We go further and extend the calculus to the situation where the Schrödinger equation admits a second-order symmetry operator, not necessarily associated with orthogonal separable coordinates. | en |

dc.format.mimetype | application/pdf | |

dc.language.iso | en | |

dc.publisher | Institute of Mathematics of the National Academy of Sciences of Ukraine | en_NZ |

dc.relation.uri | http://www.imath.kiev.ua/~snmp2003/Proceedings/miller.pdf | en |

dc.rights | This article has been published in Proceedings of Institute of Mathematics of NAS of Ukraine. ©2004 Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv(Kiev), Ukraine. | en |

dc.subject | mathematics | en |

dc.subject | Schrödinger equation | en |

dc.title | Infinite order symmetries for two-dimensional separable Schrödinger equations | en |

dc.type | Conference Contribution | en |

dc.relation.isPartOf | Fifth International Conference Symmetry in Nonlinear Mathematical Physics | en_NZ |

pubs.begin-page | 184 | en_NZ |

pubs.elements-id | 15972 | |

pubs.end-page | 195 | en_NZ |

pubs.finish-date | 2003-06-29 | en_NZ |

pubs.place-of-publication | Ukraine | en_NZ |

pubs.start-date | 2003-06-23 | en_NZ |

pubs.volume | Proceedings of Institute of Mathematics of National Academy of Sciences of Ukraine: Mathematics and its Applications Vol 50 | en_NZ |