Prove the following:(a) If two observables are compatible, their corresponding operators share a com-mon set of eigenvectors. Note: While this theorem holds for non-degenerate anddegenerate cases, you may only consider the case where the operators are non-degenerate.(b) The kinetic energy operator in H = L²(R) is defined by the actionK =ħ² d²2m dx²Let D(K) be the domain of K consisting of continuous and infinitely differentiablefunctions that vanish at infinity. For any two functions y(x) and (x) in D(K),show that (p|Ĥ) = (H). In this sense, K is said to be symmetric in itsdomain.

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Answered: eigenvectors. N

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