Problem Set 8

Due November 13

I.

a. Prove that the solutions to -cot(z) = (z₀²/z² – 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 V₀ = 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 + k² - a²)e^a(ik+a) + (2aik – k² + a²)e^a(ik-a)].