  We show that the difference of adiabatic phases, that are basis-dependent, in
noncyclic evolution of non-degenerate quantum systems have to be taken into
account to give the correct interference result in the calculation of physical
quantities in states that are a superposition of instantaneous eigenstates of
energy. To verify the contribution of those adiabatic phases in the
interference phenomena, we consider the spin-1/2 model coupled to a precessing
external magnetic field. In the model, the adiabatic phase increases in time up
to reach the difference of the Berry's phases of the model when the external
magnetic field completes a period.
