  The optical theorem is a fundamental aspect of quantum scattering theory.
Here, we generalize this theorem to the case where the incident scattering
state is a superposition of internal states of the collision partners,
introducing additional interference contributions and, e.g., providing a route
to control the total integral cross section. As in its standard form, forward
scattering plays an essential role in the generalized optical theorem, but with
interference terms being related to the inelastic forward scattering amplitudes
between states in the initial superposition. Using the resultant control index,
we show that extensive control is possible over ultracold collisions of oxygen
molecules in their rovibrational ground states, and of 85Rb-85Rb collisions,
promising systems for the first experimental demonstration of the quantum
interference control of the total scattering cross section.
