Lecticia
Sep19-07, 09:33 AM
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.
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.