Yes sorry for spamming, but I am quite confused about some of the maths of transforming operators. On the attached picture is shown the expression for an operator in a random basis in second quantization, which are combinations of anihillation and created operators weighted by matrix elements calculated in first quantization. Secondly the rules for transforming anihillation operators and creation operators are shown and lastly an expression is derived for an operator in second quantization in the position basis. Now it seems that to transform to the real space representation what is done is to simply insert the matrix elements calculated in real space representation. Is this generally how an operator transforms between bases? Shouldn't I transform the anihillation and creation operators too? Or what is the general rule for transforming operators? In another thread I used that: <vlTlv'> = ∫∫dr dr' <vlr><rlTlr'><r'lv'> But am I not supposed to transform the anihillation and creation operators too?