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Consider a spin (1/2) particle of mass m with charge 9 in an external magnetic field B. a. What is the Hamiltonian of the system? b. If S is the spin angular momentum vector, show that g = i (S x B). a. Find the eigenvalues and the corresponding eigenvectors of the following matrix: [1 2]' 2 2 b. Show that the eigenvalues can be normalized and that they are orthogonal