(a) If Atilde is a linear operator, (i is a complete, orthonormal basis, and u is an arbitrary function, show that Expand u in terms of the set (i , apply Atilde to this expansion, and then expand Atilde (i (b) If (Where the expansion coefficients wj and ui are numbers), show that the equation in (a) says that wj (iAjiui, and hence that w Au, where w, A, and u are the representatives of w, Atilde , and u Au ( jAh (hu)f

Question: (a) If Ã is a linear operator, {(i} is a complete, orthonormal basis, and u is an arbitrary function, show that Expand u in terms

(a) If Ã‚ is a linear operator, {(i} is a complete, orthonormal basis, and u is an arbitrary function, show that

Expand u in terms of the set {(i}, apply Ã‚ to this expansion, and then expand Ã‚(i. (b) If

(Where the expansion coefficients wj and ui are numbers), show that the equation in (a) says that wj = (iAjiui, and hence that w = Au, where w, A, and u are the representatives of w, Ã‚, and u.

Au-( . jAh (hu)f.

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