  We show that the geometric phase of the gyro-motion of a classical charged
particle in a uniform time-dependent magnetic field described by Newton's
equation can be derived from a coherent Berry phase for the coherent states of
the Schroedinger equation or the Dirac equation. This correspondence is
established by constructing coherent states for a particle using the energy
eigenstates on the Landau levels and proving that the coherent states can
maintain their status of coherent states during the slow varying of the
magnetic field. It is discovered that orbital Berry phases of the eigenstates
interfere coherently to produce an observable effect (which we termed "coherent
Berry phase"), which is exactly the geometric phase of the classical
gyro-motion. This technique works for particles with and without spin. For
particles with spin, on each of the eigenstates that makes up the coherent
states, the Berry phase consists of two parts that can be identified as those
due to the orbital and the spin motion. It is the orbital Berry phases that
interfere coherently to produce a coherent Berry phase corresponding to the
classical geometric phase of the gyro-motion. The spin Berry phases of the
eigenstates, on the other hand, remain to be quantum phase factors for the
coherent states and have no classical counterpart.
