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We generalize our previous unification of the Schrödinger and guidance equations in a single inhomogeneous Schrödinger equation to a Riemannian manifold with an external vector potential. A special case yields the unified theory for a spin 1 2 rigid rotator. The theory is proved to be symmetrical under the Galileo group, the unified field that integrates the particle and guiding wave being a 2-spinor.doi:10.1007/s40509-020-00234-6 fatcat:h5olkqoxyjhhdmo5hbocv7qqci