Use the WKB approximation to find the allowed energies (En) of an infinite square well wit...

Use the WKB approximation to find the allowed energies (En) of an infinite square well with a “shelf,” of height V0 extending half-way across (Figure 6.3):

Express your answer in terms of V0 and  (the nthallowedenergy for the infinite square well with no shelf). Assume that , but do not assume that En >> V0. Compare your result with what we got in Example 6.1 using first-order perturbation theory. Note that they are in agreement if either V0 is very small (the perturbation theory regime) or n is very large (the WKB—semi-classical—regime).