Prove that for a spin- (frac{1}{2}) particle in a magnetic field, Eqs. (27.29) and (27.30) imply the

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Prove that for a spin- \(\frac{1}{2}\) particle in a magnetic field, Eqs. (27.29) and (27.30) imply the Berry phase (27.32).

Data from Eq. 27.29

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Data from Eq. 27.30

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Data from Eq. 27.32

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