Constants of motion for non-differentiable quantum variational problems
KeywordsNon-differentiability, scale calculus of variations, symmetries, constants of motion, DuBois-Reymond necessary condition, Noether's theorem, Schrödinger equations
AbstractWe 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 non-differentiable problems of optimal control. As an application we obtain constants of motion for some linear and nonlinear variants of the Schrödinger equation.
How to Cite
CRESSON, Jacky, FREDERICO, Gastão S. F. & TORRES, Delfim F. M. Constants of motion for non-differentiable quantum variational problems. Topological Methods in Nonlinear Analysis [online]. 1 June 2009, T. 33, nr 2, s. 217–231. [accessed 5.12.2021].
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