2m When we write the kinetic energy operator, I = mp?, we are implicitly creating an operator that is a function of a simpler operator, p. We can generalize this to any function that can be expressed as a power series in its arguments, such as e* = 1 + x + x2 + .... (a) Suppose the wave function y(x) is an eigenfunction of the operator, , with eigenvalue a. Apply the operator, , to 4(x). Use the eigenvalue equation for A to show that y(x) is also an eigenstate of this operator and find its eigenvalue. On the quiz, you will be given values for a and n and asked to compute the result. (b) If we construct a new operator, exp(A) = 2n=0.- , one can show that (x) is also an eigenfunction of this operator. What is its eigenvalue? (On the submission quiz, you will be given a value of a and asked to compute the eigenvalue of exp(A).)