  In a time-orbiting-potential magnetic trap the neutral atoms are confined by
means of an inhomogeneous magnetic field superimposed to an uniform rotating
one. We perform an analytic study of the atomic motion by taking into account
the nonadiabatic effects arising from the spin dynamics about the local
magnetic field. Geometric-like magnetic-fields determined by the Berry's phase
appear within the quantum description. The application of a variational
procedure on the original quantum equation leads to a set of dynamical
evolution equations for the quantum average value of the position operator and
of the spin variables. Within this approximation we derive the
quantum-mechanical ground state configuration matching the classical adiabatic
solution and perform some numerical simulations.
