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 Constants of motion for non-differentiable quantum variational problems
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/4127

title: Constants of motion for non-differentiable quantum variational problems
authors: Cresson, J.
Frederico, G.S.F.
Torres, D.F.M.
keywords: Constants of motion
DuBois-Reymond necessary condition
Noether's theorem
Non-differentiability
Scale calculus of variations
Schrödinger equations
Symmetries
issue date: 2009
publisher: Juliusz Schauder University Centre
abstract: We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the scale relativity theory setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus of variations with functionals defined on sets of non-differentiable functions, as well as more general nondifferentiable problems of optimal control. As an application we obtain constants of motion for some linear and nonlinear variants of the Schrödinger equation. © 2009 Juliusz Schauder Center for Nonlinear Studies.
URI: http://hdl.handle.net/10773/4127
ISSN: 1230-3429
source: Topological Methods in Nonlinear Analysis
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