Consider a one-dimensional harmonic oscillator, with wavefunctions Un, corresponding to energies En = hw (n +=), where n=0, 1, 2, ... . Show that wavefunctions corresponding to distinct energies are "orthogonal", i.e. S , (x)um(x)dx = 0, ifn # m. Hint: make use of the relation Hun = EnUn, where H = -. h2 d2 ma 2x2 + 2m dx2 2 , and read in the textbook(s) about the property of H being a Hermitian operator