An electron is confined by a finite square well potential of height 10 eV. If E1 = 1 eV, what is the width of the well?

Question

jamesj · Answer

Good question.

I'm hoping someone can write down the relevant wave equation and boundary conditions from their head and solve this for you. (I haven't done this sort of problem for a while!)

anonymous · Answer

ok. what am looking for really is the relevant formula to use

fwizbang · Answer

Assuming E1 is the ground state, and that you can treat the well as infinitely deep
(10 eV is pretty big compared to 1 eV so the energy for the ground state should be pretty close to the infinite well value), then

E= p^2/2m ,  p = hbar k , and k=n pi/width

If you can't treat the well as infinitely deep, then you're going to have to solve the BC 
numerically, as the equation for the energies can't be solved analytically.