As mentioned at Section "Plancherel theorem", some people call this part of Plancherel theorem, while others say it is just a corollary.
This is an important fact in quantum mechanics, since it is because of this that it makes sense to talk about position and momentum space as two dual representations of the wave function that contain the exact same amount of information.
Khronos Group by Ciro Santilli 37 Updated 2025-07-16
The fact that they kept the standard open source makes them huge heroes, see also: closed standard.
Shame that many (most?) of their proposals just die out.
NP-intermediate by Ciro Santilli 37 Updated 2025-07-16
This is the most interesting class of problems for BQP as we haven't proven that they are neither:
k-transitive group by Ciro Santilli 37 Updated 2025-07-16
TODO why do we care about this?
Note that if a group is k-transitive, then it is also k-1-transitive.
This one might actually be understandable! It is what Richard Feynman starts to explain at: Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979).
The difficulty is then proving that the total probability remains at 1, and maybe causality is hard too.
The path integral formulation can be seen as a generalization of the double-slit experiment to infinitely many slits.
Feynman first stared working it out for non-relativistic quantum mechanics, with the relativistic goal in mind, and only later on he attained the relativistic goal.
TODO why intuitively did he take that approach? Likely is makes it easier to add special relativity.
This approach more directly suggests the idea that quantum particles take all possible paths.

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