Noether's Theorem with Momentum and Energy Terms for Cresson's Quantum Variational Problems

Gastão S. F. Frederico, Delfim F. M. Torres

Publication date: 12 May 2014

Abstract: 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.

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Variational principles of physics (49S05) Optimality conditions for free problems in one independent variable (49K05)

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