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In quantum chemistry, the two-electron integrals often denoted as physicist's and chemist's notations.

For spin orbital, the physicist's and chemist's notations are $$ \langle pq | rs \rangle = \int \int p(1)^* q(2)^* \frac{1}{r_{12}} r(1) s(2) d^4 x_1 d^4 x_2 $$

$$ [ pq | rs ] = \int \int p(1)^* q(1) \frac{1}{r_{12}} r(2)^* s(2) d^4 x_1 d^4 x_2 $$

respectively.

For spatial orbital, I have only found the chemist notation $$ ( pq | rs ) = \int \int p(1)^* q(1) \frac{1}{r_{12}} r(2)^* s(2) d^3 r_1 d^3 r_2 $$

Is there any physicist's notation for spatial orbital?

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    $\begingroup$ As far as Szabo/Ostlund is concerned, there's no other notation (Table 2.2, p 68). $\endgroup$ – orthocresol Apr 22 '16 at 22:51
  • $\begingroup$ yep, that's the reason for asking this question.. $\endgroup$ – Rodriguez Apr 22 '16 at 22:51
  • $\begingroup$ I guessed that that might be the case :) but that's all the info I have anyway, thought it was worth a mention anyway since you didn't mention the book. $\endgroup$ – orthocresol Apr 22 '16 at 22:53
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    $\begingroup$ Yes, there exist "physicist's notation" for integrals over spatial orbitals and symbolically it is looks the same as "physicist's notation" for integrals over spin orbital: the good-ol' Dirac bra-kets is what is usually called "physicist's notation". $\endgroup$ – Wildcat Apr 23 '16 at 12:59

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