Are the eigenfunctions of H for the particle in the one-dimensional box also eigenfunctions of the momentum

Are the eigenfunctions of Hˆ for the particle in the one-dimensional box also eigenfunctions of the momentum operator pˆ_x? Calculate the average value of p_x for the case n = 3. Repeat your calculation for n = 5 and, from these two results, suggest an expression valid for all values of n. How does your result compare with the prediction based on classical physics?