The interface of gravity and quantum mechanics illuminated by Wigner phase space

We provide an introduction into the formulation of non-relativistic quantum mechanics using the Wigner phase-space distribution function and apply this concept to two physical situations at the interface of quantum theory and general relativity: (i) the motion of an ensemble of cold atoms relevant to tests of the weak equivalence principle, and (ii) the Kasevich-Chu interferometer. In order to lay the foundations for this analysis we first present a representation-free description of the Kasevich-Chu interferometer based on unitary operators.