Bound-state Energy

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If you have 2 ions, with 2 different negative charges, in a dielectric, separated by a distance of 2a -- how do you calculate the bound-state energy of a positively charged particle subjected to this configuration?

It seems like the charge distribution due to the 2 ions would introduce an e-field in the dielectric and the interaction would manifest itself as a perturbation to the Hamiltonian... but I think that might be gettingtoo complicated.

I think I could assume a potential represented by delta functions? (Ignoring coulomb potential as I have been advised.) Does that sound reasonable? Can anyone help me flesh this out?
 

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