Analyze the bouncing ball (Problem 9.6) using the WKB approximation.
(a) Find the allowed energies, E_n, in terms of m, g, and ћ.
(b) Now put in the particular values given in Problem 9.6(c), and compare the WKB approximation to the first four energies with the “exact” results.
(c) About how large would the quantum number n have to be to give the ball an average height of, say, 1 meter above the ground?