Classical Electrodynamics · Problem 1.5

Boundary-Value Problems in Electrostatics: I — John David Jackson

Physics — E&M · hydrogen-atom-potential-charge-distribution

Problem

The time-averaged potential of a neutral hydrogen atom is given by Φ=q4πϵ0e−αrr(1+αr2)\Phi = \frac{q}{4\pi\epsilon_0} \frac{e^{-\alpha r}}{r}\left(1 + \frac{\alpha r}{2}\right) where qq is the magnitude of the electronic charge, and α−1=a0/2\alpha^{-1} = a_0/2, a0a_0 being the Bohr radius. Find the distribution of charge (both continuous and discrete) that will give this potential and interpret your result physically.

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