Apply the variation function x^2(a-x)^2 for x between 0 and a, to the particle in a box and estimate the ground state energy, E_gs.

Apply the variation function x^2(a-x)^2 for x between 0 and a, to the particle in a box and estimate the ground state energy, E_gs. Explain why the function x^2 between 0 and a cannot be used as a variation function for the particle in the box.