Let d, (x) are the energy eigenfunctions of the particle is confined in an infinite potential well and E, : nE, is the corresponding energy eigenvalues, where E, is the ground state energy. Let the particle 2ml? wavefunction is given below, V3 (x) = (x) +2(x) +$s(x) V5 (a) Show that the wavefunction w (x) is normalized. (b) Lets say we perform energy measurements. Fill the following table by calculating the probabilities of each of the given energy outputs. Energy Probability E E2 E3 E4 Rest of the energies (c) Calculate the average energy in terms of the ground state energy E., using the table above. (d) Check if the wavefunction y(x) is also the energy eigenfunction.