Question: 3.16 Let the eigenfunctions and eigenvalues of an operator be {p} and {a}, respectively, so that Apn = ann Let the function f(x) have

3.16 Let the eigenfunctions and eigenvalues of an operator A be {pnland fan), respectively, so that Apn an Let the function f (xp have the expansion t 0 Show that pn is an eigenfunction of f(A) eigenvalue f (an). That is, with

3.16 Let the eigenfunctions and eigenvalues of an operator be {p} and {a}, respectively, so that Apn = ann Let the function f(x) have the expansion f(x) = bx 1=0 Show that is an eigenfunction of f(A) with eigenvalue f(a). That is, () = f(an),

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