The dirac equation of the hydrogen atom

[Kamper]

What potential would one use when evaluating the Dirac equation of the hydrogen atom? Would it simply be in the form used when examining the hydrogen atom-Schrödinger equation or does it need modification?

 

[tom.stoer]

In non-rel. QM one starts with the same 1/r potential. What else do you have in mind?

 

[Kamper]

In non-rel. QM one starts with the same 1/r potential. What else do you have in mind?

I was just wondering that since the time-independent part of the solution is in vector form you might have to consider a potential in the form of a vector field. But maybe i´m wrong?

 

[Kamper]

Thanks for the reply by the way!

 

[Bill_K]

I was just wondering that since the time-independent part of the solution is in vector form you might have to consider a potential in the form of a vector field. But maybe i´m wrong?

Choose a gauge in which the vector potential A = 0, leaving just the Coulomb 1/r potential. Separate variables in spherical coordinates as usual, and you'll find that the four components of the Dirac spinor can be written in terms of two radial functions, leding to recursion relations, etc, etc, and solved by confluent hypergeometric functions.

 

[Kamper]

Choose a gauge in which the vector potential A = 0, leaving just the Coulomb 1/r potential. Separate variables in spherical coordinates as usual, and you'll find that the four components of the Dirac spinor can be written in terms of two radial functions, leding to recursion relations, etc, etc, and solved by confluent hypergeometric functions.

Ill try that then. Thank you!