(D) Write down a wavefunction (use ket notation) that is a normalized, 2-to-1 superposition (linear combination) of the n=1 and n=2 1D PIB wavefunctions. Prove that this state is normalized using bra-ket notation and the orthonormality of PIB wavefunctions. (E) Write down the same wavefunction you got for (D), but using the full (x) form of the 1D PIB eigenfunctions. Prove that this state is normalized by performing explicit integrations - use your result from (C)! (F) If you measure the state of the system described by the wavefunction in (D) and (E) 10,000 independent times, approximately how many times will you expect to see the system in the n=1 and n=2 states, respectively? (G) 0Show whether the wavefunction you wrote down in (E) is an eigenfunction of the 1D PIB Hamiltonian