  In relativistic quantum field theory with local interactions, charge is
locally conserved. This implies local conservation of probability for the Dirac
and Klein-Gordon wavefunctions, as special cases; and then in turn for
non-relativistic quantum field theory and for the Schroedinger and
Ginzburg-Landau equations, regarded as low energy limits. Quantum mechanics,
however, is wider than quantum field theory, as an effective model of reality.
For instance, fractional quantum mechanics and Schroedinger equations with
non-local terms have been successfully employed in several applications. The
non-locality of these formalisms is strictly related to the problem of time in
quantum mechanics. We compute explicitly for continuum wave packets the terms
of the fractional Schroedinger equation and of the non-local Schroedinger
equation by Lenzi et al. which break the local current conservation, and
discuss their physical significance. The results are especially relevant for
the electromagnetic coupling of these wavefunctions. A connection with the
non-local Gorkov equation for superconductors and their proximity effect is
also outlined.
