  We develop a framework to test the Equivalence Principle (EP) under
conditions where the quantum aspects of nature cannot be neglected,
specifically in the context of interference phenomena with unstable particles.
We derive the nonrelativistic quantum equation that describes the evolution of
the wavefunction of unstable particles under the assumption of the validity of
the EP and when small deviations are assumed to occur. As an example, we study
the propagation of unstable particles in a COW experiment, and we briefly
discuss the experimental implications of our formalism.

General Relativity and Quantum Cosmology;Quantum Physics