3. (15 points) A particle of mass m is "bouncing" up and down over a hard surface in the gravitational field. Find its WKB energy levels using the Bohr-Sommerfeld quantiza- tion condition that keeps exact value of the numerical shift coming from the phase of the WKB wave function acquired through turning points. Compare the WKB values of the first 5 levels with the exact energies given by the formula En = (2-1/3 An) (mg2h2) 1/3 where In are the zeros of the Airy function Ai(-An), X1 = 2.33811, 12 = 4.08795, 13 = 5.52056, 14 = 6.7867144, 15 = 7.94413, .... Hint: to determine the shift, figure out whether this problem admits non-rigid-non- rigid, non-rigid-rigid or rigid-rigid turning points