5.5.3.1 So­lu­tion com­plexsac-a

Ques­tion:

Are not some com­mu­ta­tors miss­ing from the fun­da­men­tal com­mu­ta­tion re­la­tion­ship? For ex­am­ple, what is the com­mu­ta­tor $[{\widehat S}_y,{\widehat S}_x]$?

An­swer:

Since the com­mu­ta­tor is an­ti­sym­met­ric, $[{\widehat S}_y,{\widehat S}_x]$ is the neg­a­tive of $[{\widehat S}_x,{\widehat S}_y]$, so it is $-{\rm i}\hbar{\widehat S}_z$.