  We investigate the behavior of an ensemble of $N$ non-interacting, identical
atoms, excited by a laser. In general, the $i$-th atom sees a Rabi frequency
$\Omega_i$, an initial position dependent laser phase $\phi_i$, and a motion
induced Doppler shift of $\delta_i$. When $\Omega_i$ or $\delta_i$ is distinct
for each atom, the system evolves into a superposition of $2^N$ intercoupled
states, of which there are $N+1$ symmetric and $(2^N-(N+1))$ asymmetric
collective states. For a collective state atomic interferometer (COSAIN) we
recently proposed, it is important to understand the behavior of all the
collective states under various conditions. In this paper, we show how to
formulate the properties of these states under various non-idealities, and use
this formulation to understand the dynamics thereof. We also consider the
effect of treating the center of mass degree of freedom of the atoms quantum
mechanically on the description of the collective states, illustrating that it
is indeed possible to construct a generalized collective state, as needed for
the COSAIN, when each atom is assumed to be in a localized wave packet. The
analysis presented in this paper is important for understanding the dynamics of
the COSAIN, and will help advance the analysis and optimization of spin
squeezing in the presence of practically unavoidable non-idealities as well as
in the domain where the center of mass motion of the atoms is quantized.
