We will consider the first order perturbation theory. In this approximation, we take unperturbed Hamiltonian as

And consider the perturbed Hamilrtonian as
Substituting in the Schrodinger Equation

We are interested to calculate the ground state energy. So both the electrons are in 1s level.
So, n = 1, l = 0 and m = 0 for both the electrons. Let us take the ground state wavefuntion of the hydrogen atom for each electron.
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