Problem Set 8

Due November 13

I.

a.
Prove that the solutions to -cot(z) = (z_{0}^{2}/z^{2}
– 1)^{1/2} give the allowed energy levels for the odd eigenfunctions of the finite square well.

b.
Determine the number of bound states available to an electron in
a finite square well with a = 1 nm and V_{0} = 9 eV.

6-42

6-53

6-61.
Hint: first solve for C
and D in terms of F, and then plug these into your equations containing A and
B. If the algebra seems excessive, you
can stop after showing that F = 4aikA/[(2aik
+ k^{2} - a^{2})e^{a(ik+}^{a)} + (2aik – k^{2} + a^{2})e^{a(ik-}^{a)}].