Note that no computations are required for this problem.
Use the correspondence principle to sketch the energy
spectrum of the allowed states 
of a particle of mass m moving
in the potential V indicated in the figure below. The
potential (marked by diamonds in the figure) consists of two simple
harmonic oscillator potentials of the same spring constant k
pasted together with a discontinuity bridging the
energies 
and 
indicated in the figure. The level of V=0
corresponds to the minimum potential in the plot.
Be sure to include the regions 
, 
and
in your sketch. For the purposed of the sketch you may assume that
there are five or so levels in each of the ranges 
and
.