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

Limits of Perturbation theory for hydrogenic atoms

  • Thread starter Cheetox
  • Start date
  • #1
23
0

Homework Statement


Why can't we use perturbation theory to calculate the effect of the spin orbit interaction in hydrogen like uranium?


Homework Equations





The Attempt at a Solution


Is it something to do with the fact that the perturbation must be small compared to the rest of the hamiltonian? But for hydrogen like uranium the ionization energy is still 28000 times that of the spin orbit shift? Or could it be to do with the fact that the bohr radius for uranium approaches the radius of the nucleus?

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
79
0
Well, I am a bit confused by your question, too.
So normally, we can obtain the EXACT result by using J operator and what not. And since we can get the exact wave function, why do we want to do it "approximately?"
The reason that Perturbation probably does not work is that, in order to get your energy, you need to know the wave function (or approximately the wave function) through the equation
E_n = <[tex]\Phi[/tex]_n l H l [tex]\Phi[/tex]_n>
We know H, it has many extra terms (especially the L dot S term)
This L dot S term made your previous wave function for Hydrogen invalid.
So without solving J and stuff like that, you actually don't really know what your phi look like (notice that this phi would not look like the original ones, ie, without the spin, because of the L dot S term). So essentially, you still need to go through solving J, and what not. And since you go through the whole thing, you can in fact get the exactly E. So I guess yes you could, it is probably just a bit redundant.
 

Related Threads for: Limits of Perturbation theory for hydrogenic atoms

Replies
0
Views
2K
Replies
10
Views
2K
  • Last Post
Replies
6
Views
2K
Replies
3
Views
11K
Replies
1
Views
4K
  • Last Post
Replies
1
Views
3K
Replies
9
Views
1K
Replies
3
Views
749
Top