How make a confront between energy levels?

[ClubDogo]

Hi there.
It is a fact that, historically, the Schrodinger Equation provides wrong energy levels for the Hydrogen Atom. The same is for The Relativistic Schrodinger Equation (hehe, this is not known by most of students, seek it in arxiv database, it was the original developed by Schrodinger that was totally relativistic, but in a second development the relativistic invariance was broken indeed for the reasons involving the inappropriate descriptionof energy levels, and Klein Gordon.
So the correct calcucus come with the Dirac Equation.
But... there is a fact.
The GREAT Arnold Sommerfeld did some high technical calculus with:
1) Special Relativity
2) Schrodinger Equation
... and come to THE SAME RESULTS OF DIRAC EQUATION FOR AN HYDROGENOIS ATOM!

I am desperately seeking for this calculations but i cannot find them anywhere, in books, in the web...
Can anyone help me?

Thankz

 

[diegzumillo]

Well, I don't know what he did. I'm curious myself now! hehe :)
but are you sure he used Schrodinger equation? because as I see, it would be create a controversy: on one side you're using relativity, and on the other side you're using a classical energy equation (through Schrodinger equation)