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This question concerns a spin-particle in a magnetic field. The Hamiltonian matrix governing this system is hw [0 Ĥ=-wSy = P d] 2 i 0 where w is the Larmor frequency. (a) Use the generalized Ehrenfest theorem to obtain an expression for the rate of change of (S) in this system, expressing your answer in terms of w and (S₂). (b) Verify that the orthonormal spinors 1 |↑y) = and y) = √2 √2 are eigenvectors of Ĥ and give their eigenvalues.