(a) Prove that if \(\psi(x)\) is a solution of the Dirac equation, Eq. (4.4.59), then it is also a solution of the Klein-Gordon equation, Eq. (4.3.12).

(b) Prove that \(\partial_{\mu}\) and \(\partial_{u}\) commute, whereas \(D_{\mu}\) and \(D_{u}\) do not. Evaluate \(\left[D_{\mu}, D_{u}\right] \psi=\) \(D_{\mu}\left(D_{u} \psi\right)-D_{u}\left(D_{\mu} \psi\right)\) and so prove 

(c) Prove that if \(\psi(x)\) is a solution of the Dirac equation in the presence of an electromagnetic field, Eq. (4.4.61), it is also a solution of a modified Klein-Gordon equation,

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= [D, Dv] i(q/hc)Fv.