Show that 
, the shift in energy of the
odd state, is exactly the average perturbation potential
experienced by a particle in the n=2 state of the unperturbed potential,
.
Determine for small values of D, the shift in energy
of the ground state, 
to lowest order in D.
Hint: For this you may find the expansion 
for 
useful.
Show that if we take the 
-function to be a very
narrow region of width 
with a large constant potential
, that the shift in energy of the ground state, to first
order, is precisely the product of the probability that a
particle in the ground state of the unperturbed well is in the
region of the -function times the value of the potential in
that region.