Imagine that an infinitely thin wall is added to the middle of a box at x = L/3. At x = L/3, the potential is infinite just as it is at x = 0 and L but the particle can tunnel through the wall because it is infinitely thin. i) write the allowed values of the wavefunction at (x=0), (x=L), and (x=L/3) and write an equation for the normalized wavefunctions that satisfy all of these boundary conditions; ii) substitute the new wavefunction expression into the Hamiltonian for the particle to find an expression for the allowed energies of the particle; and iii) graph the two lowest energy solutions and comment on the value the wavefunction is allowed to have at position x = 2L/3.