Constants of Motion for Non-Differentiable Quantum Variational Problems

Details Constants of Motion for Non-Differentiable Quantum Variational Problems Constants of Motion for Non-Differentiable Quantum Variational Problems

2008-05-06

arxiv.org/abs/0805.0720v1

Topol. Methods Nonlinear Anal. 33 (2009), no. 2, 217--231

Physics

Mathematical Physics

Partially presented at the "Fifth Symposium on Nonlinear Analysis" (SNA 2007), Torun, Poland, September 10-14, 2007. Accepted

Scientific paper

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 non-differentiable problems of optimal control. As an application we obtain constants of motion for some linear and nonlinear variants of the Schrodinger equation.

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