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Calculation of the ground state energy shift

To calculate the first order correction to the He ground state
energy, we gotta do this integral.

First, plug in the Hydrogen ground state wave function (twice).

Do the
integral and prepare the other.

The angular integrals are not hard to do.

We can do the integral for
and simplify the expression.
Because of the symmetry between
and
the rest of the integral
just doubles the result.

Jim Branson
2013-04-22