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We describe the non-relativistic time evolution of an ultra-cold degeneratequantum gas (bosons/fermions) falling in Earth's gravity during long times (10sec) and over large distances (100 m). This models a drop tower experiment thatis currently performed by the QUANTUS collaboration at ZARM (Bremen, Germany).Starting from the classical mechanics of the drop capsule and a single particletrapped within, we develop the quantum field theoretical description for thisexperimental situation in an inertial frame, the corotating frame of the Earth,as well as the comoving frame of the drop capsule. Suitable transformationseliminate non-inertial forces, provided all external potentials (trap, gravity)can be approximated with a second order Taylor expansion around theinstantaneous trap center. This is an excellent assumption and the harmonicpotential theorem applies. As an application, we study the quantum dynamics ofa cigar-shaped Bose-Einstein condensate in the Gross-Pitaevskii mean-fieldapproximation. Due to the instantaneous transformation to the rest-frame of thesuperfluid wave packet, the long-distance drop (100m) can be studied easily ona numerical grid.Comment: 18 pages latex, 5 eps figures, submitte

Dropping cold quantum gases on Earth over long times and large distances