Question

Consider a neutron in a magnetic field, fixed at an angle $\theta$ with respect to the z-axis, but rotating slowly in the $\phi$ -direction. That is, the tip of the magnetic field traces out a circle on the surface of the sphere at "latitude" $\pi-\theta .$ Explicitly calculate the Berry potential A for the spin-up state from $(5.6 .23),$ take its curl, and determine Berry's Phase $\gamma_{+} .$ Thus, verify $(5.6 .42)$ for this particular example of a curve $C$ (For hints, see "The Adiabatic Theorem and Berry's Phase" by B. R. Holstein, $A m$. J. Phys. 57(1989) 1079.)

          Consider a neutron in a magnetic field, fixed at an angle $\theta$ with respect to the z-axis, but rotating slowly in the $\phi$ -direction. That is, the tip of the magnetic field traces out a circle on the surface of the sphere at "latitude" $\pi-\theta .$ Explicitly calculate the Berry potential A for the spin-up state from $(5.6 .23),$ take its curl, and determine Berry's Phase $\gamma_{+} .$ Thus, verify $(5.6 .42)$ for this particular example of a curve $C$ (For hints, see "The Adiabatic Theorem and Berry's Phase" by B. R. Holstein, $A m$.
J. Phys. 57(1989) 1079.)

Added by -Ngel G.

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