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pls help with the two questions 4. Find the eigenvalues and eigenvectors of a5, = ((3 3!) Suppose an electron is in the spin a

pls help with the two questions

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4. Find the eigenvalues and eigenvectors of a5, = ((3 3!) Suppose an electron is in the spin a state . If S is measured, what is the probability of the result h/Z? 3' 5. Find, by explicit construction using Pauli matrices, the eigenvalues for the Hamiltonian H=?S-B for a spin E particle in the presence of a magnetic field B = 311' + 3?? + 322

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