  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.
