Consider the following wave functions (where a, b, k, and a are constants): (i) ψ(x) = a sin(kx) (iv) ψ(x) = ae-ikx (i) ψ(x) = b cos(kx) (v) ψ(x) = be+ikx (iii) ψ(x) = a/x (a) determine which of the above func- (vi) ψ(x) be-ax tions are eigenfunctions of the momentum operator, px, and identify the correspond- ing eigenvalue. (b) determine which of the above functions are eigenfunctions of the kinetic energy oper- ator, kx, and determine the corresponding eigenvalue. 4. evaluate the momentum expectation values of the free particle wavefunctions ex and etilx (where k is a positive constant). what do your results tell you about the direction in which free particles described by each of these wavefunctions are moving?