• Support PF! Buy your school textbooks, materials and every day products Here!

Potential Well

  • #1

Homework Statement


An electron is confined to a potential well of finite depth and width, 10^-9 cm. The eigenstate of highest energy of this system corresponds to the value [tex]\xi = 3.2[/tex].

a. How many bound states does this system have?
b. Estimate the energy of the ground state with respect to the zero energy line at the bottom of the well. Express answer in eV.

Homework Equations


[tex]\xi = ka[/tex] where a is half the width
[tex]\eta = \kappa a[/tex]

as far as I know k corresponds to the bound state while kappa corresponds to the unbound states

[tex]\xi tan(\xi) = \kappa[/tex] for even eigenstates
[tex]\xi cot(\xi) = -\kappa[/tex] for odd eigenstates

The Attempt at a Solution


a. Not exactly sure here.

I figured I'm looking for k but when I solve for it I get a huge number (64 million)
k = xi/a = (3.2 * 2) * 10^9

b. E = 0 at the bottom of the well so then
[tex]E = \frac{\hbar^2 \xi^2}{2ma^2}[/tex]

correct?
 

Answers and Replies

Related Threads for: Potential Well

  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
13
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
6
Views
852
Replies
9
Views
2K
  • Last Post
Replies
12
Views
5K
  • Last Post
Replies
0
Views
3K
  • Last Post
Replies
2
Views
1K
Top