Energy levels for the Hydrogen Atom

[ClubDogo]

Hello everybody.
As you surely know, the Schrödinger treatment of the Hydrogen Atom gives wrong eigenvalues for the Spectrum. The Dirac equation provides for a correct one. On the other hand, the first who found the correct expression for the levels was "mighty" Sommerfeld using a mixture of relativity, Schrödinger equation and other stuff. The question is: is there any reference for the correct calculus done as Sommerfeld did?
I solved the problem with Dirac equation but I'm curious to notice how Sommerfeld reached the same result...

Thankz

 

[dextercioby]

Not exactly the same result, a close one, he couldn't have taken account on the presence of spin for the electron, so he basically provided a relativistic theory of 2 charges attracting by means of a Coulomb electrostatic interaction and moving in closed elliptic orbits.

 

[ClubDogo]

So?

Ok... but could you write down a reference?
I'm interested in seeing this thing.

 

[dextercioby]

I haven't found anything on the internet. I'll look it up in some books.