# 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