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Pendlebury $\textit{et al.}$ [Phys. Rev. A $\textbf{70}$, 032102 (2004)] werethe first to investigate the role of geometric phases in searches for anelectric dipole moment (EDM) of elementary particles based on Ramsey-separatedoscillatory field magnetic resonance with trapped ultracold neutrons andcomagnetometer atoms. Their work was based on the Bloch equation and later workusing the density matrix corroborated the results and extended the scope todescribe the dynamics of spins in general fields and in bounded geometries. Wesolve the Schr\"odinger equation directly for cylindrical trap geometry andobtain a full description of EDM-relevant spin behavior in general fields,including the short-time transients and vertical spin oscillation in the entirerange of particle velocities. We apply this method to general macroscopicfields and to the field of a microscopic magnetic dipole.

Calculation of geometric phases in electric dipole searches with trapped spin-1/2 particles based on direct solution of the Schr\"odinger equation