Time-averaged potential of hydrogen

[cscott]

Homework Statement

The time-averaged potential of a neutral hydrogen atom is given by

$$V = \frac{q}{4 \pi \epsilon_0} \frac{e^{-\alpha r}}{r} \left ( 1 + \frac{\alpha r}{2} \right )$$

[tex]\alpha = 2/a_0[/itex], where $a_0$ is the Bohr radius.<br /> <br /> Find the charge distribution (continuous and discrete) which will give you this potential.<br /> <br /> <h2>The Attempt at a Solution</h2><br /> <br /> Totally stuck here except I think the charge density of the |1s> state should be<br /> <br /> [tex]\rho = e<1s|1s>[/itex],<br /> <br /> however that doesn't get me very far. Is the second term in V the contribution of the proton?[/tex][/tex]

 

[vela]

There's no need to think about quantum mechanics here. This is just a classical electromagnetics problem. You have a potential. Find the corresponding electric field and then take its divergence to find the charge density.