_LUL 2 114,01) = Hume Me" with n = 0, 1, 2, 3, 4, 5 where the H1100 are (real) Hermite Polynomials. For the purpose of the questions below, you do not need to use at all the actual functional form of the 111,100. You only need the expression for energy of each state and the fact that the eigenfunctions for the Harmonic Oscillator are orthonormal, i.e.: 1 if n=m In, wgswmmx = 6m: { 0 if M m The wavefunction for this particle is given by the expression: INK) = 00%00 + 011F100 + 02111200 where 3 a. Show that INK) is normalized, Le. J- |1p(x) l 2 dx = 1 b. Calculate the probability of finding the oscillator in each of the states with quantum numbers n = O, 1, 2 and 3. 9 8 .-P=P=P=~P=0 Answer 0 25, 1 2 25, 4