January 15, 1998

PHY 712 - Problem Set # 2

1.

Evaluate the ``self-energy" of an electron bound in a hydrogen atom using equations 1.52 or 1.53, with the electron density for the ground state of the hydrogen atom:

$$\rho(r) = -\frac{e}{\pi a_0^3} e^{-2r/a_0},$$ (1)

where e is the elementary charge and a₀ is the Bohr radius. Hint: Note that in Problem Set #1, you used the electrostatic potential corresponding to the ground state electronic density plus the electostatic potential of the proton.