  Unconstrained partial-wave amplitudes obtained at discrete energies from fits
to complete sets of experimental data may not vary smoothly with energy, and
are in principle non-unique. We demonstrate how this behavior can be ascribed
to the continuum ambiguity. Starting from the spinless scattering case, we
demonstrate how an unknown overall phase depending on energy and angle mixes
the structures seen in the associated partial-wave amplitudes making the
partial wave decomposition non-unique, and illustrate it on a simple toy model.
We then apply these principles to pseudo-scalar meson photoproduction and show
that the non-uniqueness effect can be removed through a phase rotation,
allowing a consistent comparison with model amplitudes. The effect of this
phase ambiguity is also considered for Legendre expansions of experimental
observables. 5 pages,
