  We present a 3D quantum mechanical theory of radio-frequency outcoupled atom
lasers from trapped atomic gases in the presence of the gravitational force.
Predictions for the total outcoupling rate as a function of the radio-frequency
and for the beam wave function are given. We establish a sum rule for the
energy integrated outcoupling, which leads to a separate determination of the
coupling strength between the atoms and the radiation field.
  For a non-interacting Bose-Einstein condensate analytic solutions are derived
which are subsequently extended to include the effects of atomic interactions.
The interactions enhance interference effects in the beam profile and modify
the outcoupling rate of the atom laser. We provide a complete quantum
mechanical solution which is in line with experimental findings and allows to
determine the validity of commonly used approximative methods.
  We also extend the formalism to a fermionic atom laser and analyze the effect
of superfluidity on the outcoupling of atoms.
