Problem on perturbation theory

[sridhar]

Homework Statement

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.

Homework Equations

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

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)$$^{2}$$ as the perturbation!

I applied the first order perturbation for the term k/r12
the correction would basically be <$$\Psi$$ /k/(r12)$$^{2}$$ / $$\Psi$$>

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

 

[Gokul43201]

Can you write down the perturbing and unperturbed hamiltonia, and the eigenfunctions of the unperturbed hamiltonian?

Why are you squaring r12?

PS: When writing down an expression/equation, it is best to LaTeX the whole thing (Example: $\langle \psi | (k/r_{12})| \psi \rangle$), rather than parts of it. Also, for using LaTeX in line with regular text, use the tags [ itex ] [ /itex ] (without spaces) instead.