Abstract
By invoking the use of a space-spin coupling transformation, the exact Schrödinger evolution wavefunction is fortunately obtained for a neutron moving in a helical magnetic field. This result just enjoys the effect of Berry's phase or its induced gauge field in Bitter-Dubbers experiment as its limiting case with strong field. It is also predicted from the exactly-dynamical analysis that a pulse of polarized neutrons with monotonous momentum will be split into two pulses with different momentum shifts accompanying the spin-down and spin-up states respectively.
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