(a) Show that the function xe ax2 is an eigenfunction of the operator (d 2 dx 2 )4a 2 x 2 What is the eigenvalue (b) Show that the function Ke r k is an eigenfunction of the operator d dr What is the eigenvalue

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Question: (a) Show that the function =xe -ax2 is an eigenfunction of the operator (d 2 /dx 2 )4a 2 x 2 . What is the

(a) Show that the function =xe^-ax2 is an eigenfunction of the operator (d²/dx²)4a²x². What is the eigenvalue? (b) Show that the function =Ke^r/k is an eigenfunction of the operator d/dr. What is the eigenvalue?

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