Talk:Bra–ket notation

Pronunciation/reading?

How do you read <a|b>? "Bracket a b", "a times b", something else? --Sigmundur (talk) 08:39, 8 March 2018 (UTC)

When the symbol inside the ket is not the name of a vector per se

The lead says "A ket looks like " | v ⟩ ". Mathematically it denotes a vector, v , "

... from which one would expect that the symbol found inside a ket would be the name of a vector. That is, take that symbol outside the ket, stick an arrow on top (or style it bold), and you have a vector in conventional notation.

However, evidently there are additional ket conventions. One is apparently to place an integer inside the ket. This is obviously not the name of a vector per se. Apparently it indicates one of the orthonormal basis vectors. So |2> indicates the second basis vector, perhaps j-hat (or e_y).

An example; https://quantum.phys.cmu.edu/CQT/chaps/cqt03.pdf page 32

Taking this further, some authors apparently may place a variable inside the ket, such as | n >, to indicate the nth basis vector, perhaps useful in a summation. But that is indistinguishable syntactically from the normal ket usage, and mistakenly suggests that n might be a vector.

At any rate, because a reader may well be visiting the page to try to interpret the bra-ket notation they've newly encountered written somewhere, it would be helpful if variants such as the one I just described could be discussed in the article in an orderly fashion. Gwideman (talk) 15:54, 22 February 2021 (UTC)

I strongly believe this would be overkill, but, of course, if somebody proposed redress here, on this page, before editing the page, its adequacy or defects could be vetted. IMO, a sensible, perceptive, well-meaning reader could not be confused, and could adapt the notation as circumstances dictated. This article is not a tutorial, and is meant to summarize/refresh basic facts one has already been taught at some level, e.g. in a course that then bears the onus of miscommunication. There is an extreme and present danger of burdening the article with lots of fussing distractions making it unreadable to all but the dedicated pedant reader, thereby furthering the degradation process... Cuzkatzimhut (talk)

Thanks for responding, but I am very puzzled by your remarks. I do not understand how, in an article titled "Bra-ket notation", the subject of common variations in the syntax of the notation could possibly be overkill. Your second sentence ("IMO...") I do not understand at all -- are you referring to the page as currently, or as potentially revised? And what does "well meaning" have to do with the current discussion? Sure, articles on Wikipedia are not tutorials. They are pages in an encyclopedia. But then you go on to say it's meant to review facts that the reader is presumed to have learned previously. No, it's a page in an encyclopedia. Wikipedia:Wikipedia is an encyclopedia You conjure up some previous course in which there was miscommunication -- apropos of what? I might concur that there's a risk of articles becoming cluttered with distractions. Right now it's chock full of applications and examples in which Bra-ket notation is used, related only secondarily to the notation per se (but not unwelcome), yet somehow you are resistant to the idea of bolstering the description of the notation itself, which would actually improve the signal-to-noise ratio. Gwideman (talk) 23:19, 25 February 2021 (UTC)

I'm never resistant to the idea of improving the article! How could I be? I would like to be resistant to its routine abuses: of course, I've been watching with horror its runaway descent into mush, by "bold" hit-or-miss "improvers". Notation like $|n\rangle$ is self-explanatory, since what goes in the ket, most of the time, is the eigenvalue of the operator specifying the basis, like position, momentum, etc, as clarified in section 3.1, just about the only meaningful section in the article; in this case, the number operator N, s.t. $N|n\rangle =n|n\rangle$. If you wished to think of it as the cardinal index of a basis vector, of course it would tag the n+1-th vector since the counting starts from n = 0. In any case, the power of kets is maintaining flexibility and abstraction, and not merely rewriting vectors, for which there exist excellent notations. Dirac introduced them precisely so detailed pedantic questions about them could be bypassed, once their formal properties are completely specified. Physics has never looked back. Cuzkatzimhut (talk) 01:34, 26 February 2021 (UTC)

Well, this discussion is related to the heading explaining that "the mathematicians" do it all so differently. It is true that mathematicians rather redefine the scope of existing notation, so that it retains its familiar meaning vis a vis the basic stuff (e.g. linear algebra 101) but also works in the more advanced stuff (linear functional analysis 101), depending on the spaces specified. But most mathematicians who do functional analysis (and adjacent such as integral eqns, PDEs etc) are quite conversant with Dirac notation as well and may even use it when the mood strikes. A distinct drawback of conventional notation is that sometimes the index is the salient part and the variable glyph itself an unimportant dummy - Dirac allows you, effectively, to insert the index inside the | > moreover, Dirac notation has the Riesz-Frechet theorem and the notion of an observation as being an operator baked right into it. One can see why physicists like this very much and wax (somewhat too) lyrically about its "power". Others may prefer to establish everything in conventional notation - just to make sure there is no sleight of hand! 2A01:CB0C:CD:D800:C5C0:901B:9EDE:87D8 (talk) 12:44, 17 March 2021 (UTC)

Outer product

Interesting the way |ψ><ψ| has a crossing X like ⊗ in the middle. Starple (talk) 23:10, 26 March 2021 (UTC)

Removed Request For Simplified Lead In

Removed request after providing the information.

Hopefully the simplification is acceptable because the topic loses something important if any further condensing is done. Astrojed (talk) 03:07, 5 February 2023 (UTC)

Provided a lead section and removed the notice of it missing.

This is a highly technical topic used in some quantum mechanics. A general practitioner of science may understand it if somewhat knowledgeable about quantum mechanics, complex numbers, vector products, and matrix algebra. A well qualified editor might make the improvements that are requested. Astrojed (talk) 08:46, 11 February 2023 (UTC)

Article issues and classification

The article has a "may be in need of reorganization" tag but also has unsourced sentences, paragraphs, subsections, and sections.

The B-class criteria #1 states; The article is suitably referenced, with inline citations. It has reliable sources, and any important or controversial material which is likely to be challenged is cited. The article needs a reassessment.

The article is reasonably well-written. (#4). The issues are not indicative of "well-written". -- Otr500 (talk) 08:43, 27 February 2023 (UTC)