Description

• Title:
  Constants of motion for non-differentiable quantum variational problems
• Creator:
  Cresson, Jacky;
  Frederico, Gastão S. F.;
  Torres, Delfim F. M.
• Description:
  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 Schrödinger equation.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2009.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 33, No 2 (June 2009); 217 - 231;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.015/8605
• Subject:
  Non-differentiability;
  scale calculus of variations;
  symmetries;
  constants of motion;
  DuBois-Reymond necessary condition;
  Noether's theorem;
  Schrödinger equations;
  49K05;
  49S05;
  26B05;
  81Q05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.015
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other