# Klein-Gordon-Schrodinger and Dirac equations

1. Sep 19, 2007

### Lecticia

1. The problem statement, all variables and given/known data
I need to solve the Klein-Gordon-Schrodinger and the Dirac equation for the Coulombian potential.

2. Relevant equations

KGS:
$$[(\partial^{\mu}\partial_{\mu} + m^2c^2/h^2)\Psi=0$$
I don't know how I can add the potential term...

Dirac:
$$[\gamma^{\mu}(ih\partial_{\mu} - (e/c) A_{\mu})-mc)]\Psi=0$$

3. The attempt at a solution

I'm trying to do something with these equations in order to make them with a Schrodinger-like form. For the Dirac eq., I found the hydrogen atom resolved in Sakurai's book, but I could not understand what they did (they took about 10 pages) and I wonder if there is another (easier) way to do this.

Last edited: Sep 19, 2007
2. Sep 19, 2007

### dextercioby

There really isn't anu other way. A book solving both equations for the Coulomb potential is Greiner's "Relativistic Quantum Mechanics - Wave equations".

3. Sep 19, 2007

### Lecticia

Thanks. I'll look for this book online, 'cos I don't have it... :(