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hi everyone here ,

i have a problem about the exhange energy .

IN quantum mechanics, there is a example how to solve eigenvalue and eigenfunction of helium within the framework of perturbation theory .

when two electrons are in different eigenstates,the first order correction of energy is :E(1)=k+(-)J

K:coulomb energy

and J is exhcange energy

when + : spin anti-parallel

and -: spin parallel

and recently i have read about hartree-fock theory ,and found the exchange-energy exists only spin-parallel. Exchange integrals additionally arise if the electrons are of the same spin

so my problen is why there is inconsistency between them ?

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# Help about the exchange energy

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