(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine approximately the ground state energy of a helium like atom using first order perturbation theory in the electron-electron interaction.

Ignore the spins of the electrons and the Pauli principle.

2. Relevant equations

given that [tex]\int[/tex]d[tex]\tau[/tex]1[tex]\int[/tex]d[tex]\tau[/tex]2 e[tex]^-(r1+r2){}[/tex]/r1+r2 = 20[tex]\Pi[/tex][tex]^{2}[/tex]

3. The attempt at a solution

Consider a system where electron1-electron2 distance = r12

electron1-nucleus distance= r1

electron2-nucleus distance= r2

The S.E of this system would be exactly solvable if the term containing r12 disappears from the hamiltonian. Therefore we treat k/(r12)[tex]^{2}[/tex] as the perturbation!

I applied the first order perturbation for the term k/r12

the correction would basically be <[tex]\Psi[/tex] /k/(r12)[tex]^{2}[/tex] / [tex]\Psi[/tex]>

And i am stuck! Cant understand what to do next!

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# Homework Help: Problem on perturbation theory

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