The Lagrangian form of the Schrödinger equation is useful in the identification of the quantum energy, momentum and angular momentum, which are the conserved quantities suggested by the Noether’s theory of invariants.

On the other hand, the charge and current densities in classical electrodynamics correspond to derivatives of the Lagrangian density with respect to the Maxwell potentials. Respectively, to identify correctly the quantum charge and current, one should introduce the Lagrangian density depending on the wave function ψ and on the Maxwell potentials. This Lagrangian density should correspond to the coupled Maxwell–Schrödinger equations.


  1. 43.
    P.A.M. Dirac, Proc. R. Soc. A 112, 661 (1926) ADSzbMATHCrossRefGoogle Scholar
  2. 72.
    C. Gérard, Scattering theory for Klein–Gordon equations with non-positive energy. arXiv:1101.2145

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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Alexander Komech
    • 1
  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria

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