please answer and explain all parts, thank you

2) The Hamiltonian operator for a particular one-dimensional system of mass m that is "free", in the sense that there is no potential energy dependent on the one-dimensional position coordinate x, is H = T (i.e., V =0). (a) Show that the set of functions w; = sin(jx) + icos(jx) where j = +1, 2, 3, ... are eigenfunctions of both H and of the one-dimensional momentum operator. (b) What are the expectation values for / and p for the j = 5 stationary state? Note that since the eigenfunctions in this case are not normalized, the expectation value for a given operator A is defined as (A ) = (c) What is the relationship between these two expectation values