200:
95:
643:
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 | : -->
85:
64:
31:
352:
279:
190:
169:
22:
766:
694:
514:
the page as currently, or as potentially revised? And what does "well meaning" have to do with the current discussion? Sure, articles on
Knowledge 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.
622:= 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.
513:
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
642:
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
518:
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
644:
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 -
497:
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
814:
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.
469:
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.
533:
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
445:
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:
442:... 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.
360:
291:
566:, 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
896:
646:
519:
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.
466:, 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.
151:
35:
616:
886:
926:
901:
560:
844:
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.
712:
256:
911:
141:
921:
881:
246:
618:. 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
891:
776:
515:
117:
199:
906:
367:
363:
303:
298:
222:
650:
916:
801:
730:
108:
69:
835:
The article has a "may be in need of reorganization" tag but also has unsourced sentences, paragraphs, subsections, and sections.
876:
743:
Hopefully the simplification is acceptable because the topic loses something important if any further condensing is done.
213:
174:
44:
839:
376:
315:
489:
editing the page, its adequacy or defects could be vetted. IMO, a sensible, perceptive, well-meaning reader
573:
485:
I strongly believe this would be overkill, but, of course, if somebody proposed redress here, on this page,
627:
503:
50:
94:
21:
520:
471:
417:
221:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
116:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
820:
748:
524:
475:
381:
321:
100:
84:
63:
537:
671:
623:
499:
857:
461:
Taking this further, some authors apparently may place a variable inside the ket, such as |
396:
378:
351:
336:
317:
278:
413:
205:
870:
816:
744:
493:
be confused, and could adapt the notation as circumstances dictated. This article is
861:
824:
752:
675:
654:
631:
528:
479:
421:
667:
455:
853:
189:
168:
113:
195:
90:
380:
319:
765:
498:
dedicated pedant reader, thereby furthering the degradation process...
218:
427:
When the symbol inside the ket is not the name of a vector per se
757:
Provided a lead section and removed the notice of it missing.
759:
687:
382:
345:
322:
272:
15:
852:(#4). The issues are not indicative of "well-written". --
783:
708:
447:
indicates the second basis vector, perhaps j-hat (or e
897:
Knowledge level-5 vital articles in
Physical sciences
576:
540:
217:, a collaborative effort to improve the coverage of
112:, a collaborative effort to improve the coverage of
703:
may be too technical for most readers to understand
685:Removed request after providing the information.
610:
554:
562:is self-explanatory, since what goes in the ket,
456:https://quantum.phys.cmu.edu/CQT/chaps/cqt03.pdf
412:? "Bracket a b", "a times b", something else? --
666:<ψ| has a crossing X like ⊗ in the middle.
645:just to make sure there is no sleight of hand!
887:Knowledge vital articles in Physical sciences
390:This page has archives. Sections older than
330:This page has archives. Sections older than
8:
605:
588:
549:
927:C-Class physics articles of High-importance
902:C-Class vital articles in Physical sciences
435:⟩ ". Mathematically it denotes a vector,
163:
58:
802:Learn how and when to remove this message
731:Learn how and when to remove this message
715:, without removing the technical details.
597:
580:
575:
541:
539:
850:The article is reasonably well-written.
611:{\displaystyle N|n\rangle =n|n\rangle }
165:
60:
19:
849:
843:
681:Removed Request For Simplified Lead In
516:Knowledge:Knowledge is an encyclopedia
400:when more than 5 sections are present.
340:when more than 5 sections are present.
713:make it understandable to non-experts
647:2A01:CB0C:CD:D800:C5C0:901B:9EDE:87D8
7:
431:The lead says "A ket looks like " |
211:This article is within the scope of
106:This article is within the scope of
49:It is of interest to the following
14:
912:Mid-priority mathematics articles
846:The article needs a reassessment.
830:Article issues and classification
394:may be automatically archived by
334:may be automatically archived by
126:Knowledge:WikiProject Mathematics
922:High-importance physics articles
882:Knowledge level-5 vital articles
786:by adding one in your own words.
764:
692:
350:
277:
198:
188:
167:
129:Template:WikiProject Mathematics
93:
83:
62:
29:
20:
251:This article has been rated as
146:This article has been rated as
892:C-Class level-5 vital articles
598:
581:
542:
1:
862:08:43, 27 February 2023 (UTC)
825:08:46, 11 February 2023 (UTC)
632:01:34, 26 February 2021 (UTC)
529:23:19, 25 February 2021 (UTC)
480:15:54, 22 February 2021 (UTC)
231:Knowledge:WikiProject Physics
225:and see a list of open tasks.
120:and see a list of open tasks.
907:C-Class mathematics articles
753:03:07, 5 February 2023 (UTC)
701:This article's lead section
665:Interesting the way |ψ: -->
411:How do you read <a|b: -->
234:Template:WikiProject Physics
943:
676:23:10, 26 March 2021 (UTC)
655:12:44, 17 March 2021 (UTC)
555:{\displaystyle |n\rangle }
257:project's importance scale
422:08:39, 8 March 2018 (UTC)
388:
348:
250:
183:
145:
78:
57:
917:C-Class physics articles
152:project's priority scale
109:WikiProject Mathematics
877:C-Class vital articles
612:
556:
407:Pronunciation/reading?
613:
557:
36:level-5 vital article
784:improve this article
574:
538:
132:mathematics articles
214:WikiProject Physics
608:
552:
101:Mathematics portal
45:content assessment
812:
811:
804:
741:
740:
733:
404:
403:
344:
343:
309:
308:
271:
270:
267:
266:
263:
262:
162:
161:
158:
157:
934:
840:B-class criteria
807:
800:
796:
793:
787:
768:
760:
736:
729:
725:
722:
716:
696:
695:
688:
617:
615:
614:
609:
601:
584:
564:most of the time
561:
559:
558:
553:
545:
399:
383:
354:
346:
339:
323:
295:
294:
281:
273:
239:
238:
237:physics articles
235:
232:
229:
208:
203:
202:
192:
185:
184:
179:
171:
164:
134:
133:
130:
127:
124:
103:
98:
97:
87:
80:
79:
74:
66:
59:
42:
33:
32:
25:
24:
16:
942:
941:
937:
936:
935:
933:
932:
931:
867:
866:
832:
808:
797:
791:
788:
781:
769:
737:
726:
720:
717:
709:help improve it
706:
697:
693:
683:
663:
572:
571:
536:
535:
450:
429:
409:
395:
384:
379:
335:
324:
318:
286:
253:High-importance
236:
233:
230:
227:
226:
204:
197:
178:High‑importance
177:
131:
128:
125:
122:
121:
99:
92:
72:
43:on Knowledge's
40:
30:
12:
11:
5:
940:
938:
930:
929:
924:
919:
914:
909:
904:
899:
894:
889:
884:
879:
869:
868:
865:
864:
847:
836:
831:
828:
810:
809:
772:
770:
763:
739:
738:
700:
698:
691:
682:
679:
662:
659:
658:
657:
639:
638:
637:
636:
635:
634:
607:
604:
600:
596:
593:
590:
587:
583:
579:
551:
548:
544:
508:
507:
448:
428:
425:
408:
405:
402:
401:
389:
386:
385:
377:
375:
372:
371:
356:
342:
341:
329:
326:
325:
320:
316:
314:
311:
310:
307:
306:
301:
288:
287:
282:
276:
269:
268:
265:
264:
261:
260:
249:
243:
242:
240:
223:the discussion
210:
209:
206:Physics portal
193:
181:
180:
172:
160:
159:
156:
155:
144:
138:
137:
135:
118:the discussion
105:
104:
88:
76:
75:
67:
55:
54:
48:
26:
13:
10:
9:
6:
4:
3:
2:
939:
928:
925:
923:
920:
918:
915:
913:
910:
908:
905:
903:
900:
898:
895:
893:
890:
888:
885:
883:
880:
878:
875:
874:
872:
863:
859:
855:
851:
848:
845:
841:
837:
834:
833:
829:
827:
826:
822:
818:
806:
803:
795:
792:February 2023
785:
779:
778:
773:This article
771:
767:
762:
761:
758:
755:
754:
750:
746:
735:
732:
724:
714:
710:
704:
699:
690:
689:
686:
680:
678:
677:
673:
669:
661:Outer product
660:
656:
652:
648:
641:
640:
633:
629:
625:
621:
602:
594:
591:
585:
577:
569:
565:
546:
532:
531:
530:
526:
522:
517:
512:
511:
510:
509:
505:
501:
496:
492:
488:
484:
483:
482:
481:
477:
473:
467:
464:
459:
457:
452:
443:
440:
438:
434:
426:
424:
423:
419:
415:
406:
398:
393:
387:
374:
373:
370:
369:
365:
362:
357:
355:
353:
347:
338:
333:
328:
327:
313:
312:
305:
302:
300:
297:
296:
293:
290:
289:
285:
280:
275:
274:
258:
254:
248:
245:
244:
241:
224:
220:
216:
215:
207:
201:
196:
194:
191:
187:
186:
182:
176:
173:
170:
166:
153:
149:
143:
140:
139:
136:
119:
115:
111:
110:
102:
96:
91:
89:
86:
82:
81:
77:
71:
68:
65:
61:
56:
52:
46:
38:
37:
27:
23:
18:
17:
813:
798:
789:
777:lead section
774:
756:
742:
727:
718:
702:
684:
664:
624:Cuzkatzimhut
619:
567:
563:
500:Cuzkatzimhut
494:
490:
486:
468:
462:
460:
454:An example;
453:
444:
441:
436:
432:
430:
410:
391:
358:
349:
331:
283:
252:
212:
148:Mid-priority
147:
107:
73:Mid‑priority
51:WikiProjects
34:
842:#1 states;
397:ClueBot III
337:ClueBot III
123:Mathematics
114:mathematics
70:Mathematics
871:Categories
359:Archives:
491:could not
414:Sigmundur
304:Archive 2
299:Archive 1
39:is rated
817:Astrojed
745:Astrojed
721:May 2022
521:Gwideman
472:Gwideman
458:page 32
284:Archives
782:Please
775:has no
707:Please
668:Starple
570:, s.t.
392:90 days
332:90 days
255:on the
228:Physics
219:Physics
175:Physics
150:on the
41:C-class
854:Otr500
487:before
47:scale.
465:: -->
361:Index
292:Index
28:This
858:talk
838:The
821:talk
749:talk
672:talk
651:talk
628:talk
525:talk
504:talk
476:talk
439:, "
418:talk
247:High
711:to
495:not
451:).
446:-->
142:Mid
873::
860:)
823:)
751:)
674:)
653:)
630:)
606:⟩
589:⟩
550:⟩
527:)
478:)
420:)
366:,
856:(
819:(
805:)
799:(
794:)
790:(
780:.
747:(
734:)
728:(
723:)
719:(
705:.
670:(
649:(
626:(
620:n
603:n
599:|
595:n
592:=
586:n
582:|
578:N
568:N
547:n
543:|
523:(
506:)
502:(
474:(
463:n
449:y
437:v
433:v
416:(
368:2
364:1
259:.
154:.
53::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
