Noether's Theorem with Momentum and Energy Terms for Cresson's Quantum   Variational Problems
  We prove a DuBois-Reymond necessary optimality condition and a Noether symmetry theorem to the recent quantum variational calculus of Cresson. The results are valid for problems of the calculus of variations with functionals defined on sets of nondifferentiable functions. As an application, we obtain a constant of motion for a linear Schrodinger equation. 
Gastao S. F. Frederico, Delfim F. M. Torres
math.OC math-ph math.MP