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Recently I have asked this question: Why cannot I simplify with the same phase factor from a sum of states

However, I think the title doesn't capture well the crux of the matter: it seems like a quantum-specific question, whereas the problem is something more fundamental.

What title could I use to make it more appealing to a wider range of answerers, not just quantum physicists?

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    $\begingroup$ I don't know about the title but 1) for the body, you should not use acronyms; it so happens that I know what a Schrödinger equation is, so I could guess taht TDSE meant time dependent Schrödinger equation. 2) It may or may not be better if you rephrased in terms of the usual mathematical notation for vector spaces, instead of bra-ket notation, which i can barely understand (and I may not be alone) Or perhaps post in physics.SE $\endgroup$ Jun 6 at 11:57
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    $\begingroup$ 3) Your question looks to me, as someone who knows basically no (quantum or otherwise) physics like this: $$ 1 \times 1 + 2\times 2 + 0\times 3 = 0 \times 1 + 0\times 2 + 1 \times 3 $$ why can't we cancel the factors on the right? If we do this, we get $$ 1 + 2 + 0 = 0 + 0 + 1$$ which is wrong? $\endgroup$ Jun 6 at 11:58
  • $\begingroup$ Thank you for both points, especially the third, that makes the issue clear. $\endgroup$
    – zabop
    Jun 6 at 12:04
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    $\begingroup$ It seems someone who could wade through the physics more confidently than me has written much the same in an answer you accepted :) anyway, glad to help $\endgroup$ Jun 6 at 12:06
  • $\begingroup$ You guys rock indeed. $\endgroup$
    – zabop
    Jun 6 at 12:07
  • $\begingroup$ ....the example above is wrong :):):):) I guess it would have been enough to use $ 2\times 1 + 0 \times 2 = 0 \times 1 + 1\times2$. Sorry, but anyway its sorted now $\endgroup$ Jun 6 at 12:09
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    $\begingroup$ Oh because even the first line one doesn't hold? :) Forgot to check that, but nevertheless it made the point! :) $\endgroup$
    – zabop
    Jun 6 at 12:12

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