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(a) Prove [A, bB+cC] = b[A, B]+c[A, C], where b and c are constants. (b) Prove...

(a) Prove [A, bB+cC] = b[A, B]+c[A, C], where b and c are constants. (b) Prove [AB, C] = A[B, C] +[A, C]B. (c) Use the last relation to work out the commutator [x^2 , p], given that [x, p] = i¯h. (d) Work out the result of [x 2 , p]f(x) directly, by computing the effect of the operators on f(x), and confirm that this agrees with your answer to (c). [12]

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