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Stäckel multipliers in Euclidean space
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology. Univ.,.
2000 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

In order to apply the method of separation of variables to the natural Hamilton-Jacobi equation !  = E in Euclidean space, one has to find new curvilinear coordinates  in which the transformed equation admits a complete separated solution u(x) = . For a potential V(q) given in Cartesian coordinates, the main difficulty is to decide if such a transformation x(q) exists and to effectively determine it explicitly. Surprisingly, this nonlinear problem has a complete algorithmic solution, which we present here. It is based on recursive use of the Bertrand-Darboux equations, which are linear second order partial differential equations with undetermined coefficients. The results applies to the Helmholtz (stationary Schrödinger) equation as well.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 2000. , p. 77
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 833
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-145905Local ID: LiU-TEK-LIC-2000:29ISBN: 9172197781 (print)OAI: oai:DiVA.org:liu-145905DiVA, id: diva2:1200208
Available from: 2018-04-23 Created: 2018-04-23 Last updated: 2018-12-04Bibliographically approved

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Waksjö, Claes

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