# Atomic spectra evidence for relativistic potential

1. Dec 25, 2005

### QMrocks

In L. I. Schiff book, one can follow his derivation of the Hamiltonian from Dirac relativistic equation and obtain the following..
$$\left[\frac{\vec{p}^2}{2m}+V-\frac{\hbar^2}{4m^{2}c^{2}}\frac{dV}{dr}\frac{\partial}{\partial r}+\frac{1}{2m^{2}c^{2}}\frac{1}{r}\frac{dV}{dr}\vec{S}\cdot \vec{L}\right]\Psi_{2}=E'\Psi_{2}$$
where $$\vec{S}=(\hbar/2)\vec{\sigma}$$ and $$\vec{L}=\vec{r}\times \vec{p}$$.
He mentioned in his text that the third term is a result of relativistic correction to the potential energy. He also comment that this term is more difficult to demonstrate experimentally than the spin orbit energy. Can someone update me on the experimental progress on this aspect?

Last edited: Dec 25, 2005
2. Dec 31, 2005

### QMrocks

just bumping it up to see if someone can help..

3. Dec 31, 2005

### ZapperZ

Staff Emeritus
Didn't mean to ignore your question, but since I'm on vacation, I don't have access to the online journals and searches. Google Scholar works, but one really needs full access to the articles to answer your question.

Hopefully, someone else may already have a ready answer to this.

Zz.

4. Jan 1, 2006

### QMrocks

Thanks Zapper. i tried to search the internet abt that. But i retrieve bunch of results not really pertaining to what i want. Just wondering if that 3rd term in the equation has a name? i search for 'relativistic correction to potential energy' and it does not help...