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)ea(ik+a) + (2aik k2 + a2)ea(ik-a)].