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Rewriting the transition amplitude, third step

With Oλμ=jpjqp||Oλ||qλ1[ajp˜ajq]λμ, we can write ΦJM|Oλμ|ΦJM=pqp|Oλμ|qΦJM|apaq|ΦJM, as ΦJM|Oλμ|ΦJM=jpjqp||Oλ||qΦJM|λ1[ajp˜ajq]λμ|ΦJM. We have suppressed the summation over quantum numbers like np,nq etc.