A set of “spherical vector” operators ?? (? = ±1,0)
is defined by its commutation relations with a set of angular
momentum operators:
[?? , ??] = ℏ???
[?±,??] = ℏ√((1 − ?)(2 ± ?))
??±1
Could ?± and ?? be considered a set of
spherical vector operators themselves, when scaled by some
appropriate constants? If no, demonstrate which commutation
relation they fail to satisfy. If yes, write
?1,?0, ?−1 in terms of the angular
momentum operators, and show that...