free particle of mass, m in a 1 dimensional box, V(x)=0

a wave function given by y(x) = Aeikx + Be-ikx, and its time independent Schrodinger equation is (mm) 4(x) = EP(x). h2 d2 2m dx2 2mE = Aeikx + Be-lkx is a general solution where k = 12 (a). Show that ''(x) (Hint: Derive the energy value for a free particle) (b). Consider the two cases where A=0 and then where B=0. Determine if these wavefunctions are (separately) eigenfunctions of the momentum operator and, if So, what the eigenvalues are