  We derive a model-independent expression for finite-volume matrix elements.
Specifically, we present a relativistic, non-perturbative analysis of the
matrix element of an external current between a one-scalar in-state and a
two-scalar out-state. Our result, which is valid for energies below
higher-particle inelastic thresholds, generalizes the Lellouch-Luscher formula
in two ways: we allow the external current to inject arbitrary momentum into
the system and we allow for the final state to be composed an arbitrary number
of strongly coupled two-particle states with arbitrary partial waves (including
partial-wave mixing induced by the volume). We also illustrate how our general
result can be applied to some key examples, such as heavy meson decays and
meson photo production. Finally, we point out complications that arise
involving unstable resonance states, such as $B\rightarrow K^*\ell^+\ell^-$
when staggered or mixed-action/partially-quenched calculations are performed.
