  We present a generalized model for the evolution of atomic wave-packets in
matter-wave interferometers. This method provides an efficient tool for
analyzing the performance of atomic interferometers using atom clouds prepared
in a trap as a Bose-Einstein condensate (BEC) or as a thermal ensemble.
Predictions of the model for dynamic properties such as wave-packet size and
phase are in excellent agreement with explicit numerical solutions of the
non-linear Gross-Pitaevskii equations and enable fast calculations of
interferometric performance in regimes where full numerical solutions become
impractical. As a starting point, the static Thomas-Fermi (TF) approximation
for a BEC in a harmonic trap is generalized to the whole range of atom-atom
interaction strengths: from non-interacting atoms (low densities) to the
standard TF limit (high atomic densities, as long as the condensate
approximation still holds). In particular, this generalization allows a good
estimation of atomic cloud properties along the transition from a
three-dimensional to a quasi-one-dimensional BEC in an elongated trap. We then
develop a theoretical model of wave-packet evolution in time-dependent
conditions. The model is applicable for a wide range of dynamical problems
involving evolution in time-dependent potentials and in a changing mean-field
atomic repulsion due to splitting and separation of wave-packets. We use the
model for studying two effects that influence interferometric coherence:
imperfect spatial recombination in a two-state interferometer (the so-called
"Humpty-Dumpty effect") and phase diffusion due to number uncertainty in the
two interferometer arms, which was previously studied thoroughly only for
interferometric schemes where the BECs in the two arms stay trapped (for
example, in a double-well potential).
