# Super-Lagrangian and variational principle for generalized continuity equations

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 ##IMG##
[http://ej.iop.org/images/1751-8121/52/15/155203/aab082fieqn001.gif] -phase symmetry of the standard
Lagrangian, the generalized continuity equations derived here, are based on a non-abelian ##IMG##
[http://ej.iop.org/images/1751-8121/52/15/155203/aab082fieq...]