Timeline for A paradox in using completeness relation $\sum |\rangle\langle|=1$ of quantum mechanics

10 events

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Oct 27 at 13:16	comment	added	Attended		I think it is just Eqn. (4), two "2" are independent. Like tensor contraction between $A = a_i e^i$, $B = b^i e_i$. If we compute $AB$, better rename as $i$ and $j$. Also, in Eqn. (4), if insert completeness relation, name two "2" as "2" and "3".
Oct 27 at 12:48	comment	added	Attended		Up to (4) seems ok, numerically. Step (3) is just renaming variable. So Eqn. (4) expresses 3 particles into two-particle operations. Eqn. (5) is odd. That is the problem. It may be understood as $\int dr_1 \int dr_2 \phi_p(1)^* \phi_q(2)^* r_{12} \phi_q (2)\phi_r(2)^* r_{12}^{-1} \phi_p(1) \phi_r(2) $.
Oct 27 at 12:27	comment	added	Quillo		Seems you're just lost in notation; there is no paradox. If you have 3 particles, you can't conflate their Hilbert spaces.
Oct 27 at 12:25	comment	added	Tobias Fünke		Eq. $(5)$ does not make sense at all, mathematically. (at least in the usual understanding of the notation).
Oct 27 at 12:15	history	edited	Qmechanic♦	CC BY-SA 4.0	added 1 character in body; edited tags
Oct 27 at 11:58	history	edited	Michael Seifert	CC BY-SA 4.0	Added \tag commands in MathJaX for legibility
Oct 27 at 11:56	history	edited	Attended	CC BY-SA 4.0	edited title
Oct 27 at 11:55	history	edited	Attended	CC BY-SA 4.0	edited title
S Oct 27 at 11:55	review	First questions
Oct 27 at 11:58
S Oct 27 at 11:55	history	asked	Attended	CC BY-SA 4.0