Sketch the first three eigenstates for the potential
. By counting the number of wavelengths
which occur in a complete orbit between the classical turing
points, give a better estimate (than that they simply be
integer multiples of Planck's constant h) of the expected values of
the classical action integral of the SHO, 
, in allowed orbits. What does your
amended Bohr-Sommerfeld condition give for the allowed energies of the
SHO?