• DOI:10.1088/1751-8121/ab082f
• Corpus ID: 53630647

Super-Lagrangian and variational principle for generalized continuity equations

@article{Diakonos2019SuperLagrangianAV,
  title={Super-Lagrangian and variational principle for generalized continuity equations},
  author={Fotis K. Diakonos and Peter Schmelcher},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2019}
}

• F. Diakonos, P. Schmelcher
• Published 7 November 2018
• Mathematics, Physics
• Journal of Physics A: Mathematical and Theoretical

We present a variational approach which shows that the wave functions belonging to quantum systems in different potential landscapes, are pairwise linked to each other through a generalized continuity equation. This equation contains a source term proportional to the potential difference. In case the potential landscapes are related by a linear symmetry transformation in a finite domain of the embedding space, the derived continuity equation leads to generalized currents which are divergence free within this spatial domain. In a single spatial dimension these generalized currents are invariant. In contrast to the standard continuity equation, originating from the abelian $U(1)$-phase symmetry of the standard Lagrangian, the generalized continuity equations derived here, are based on a non-abelian $SU(2)$-transformation of a Super-Lagrangian. Our approach not only provides a rigorous theoretical framework to study quantum mechanical systems in potential landscapes possessing local symmetries, but it also reveals a general duality between quantum states corresponding to different Schr\"{o}dinger problems.