A set of “spherical vector” operators ?? (? = ±1,0) is defined by its commutation relations...

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 they satisfy all relevant relations.

Expert Solution

genius_generous answered 2 years ago

Vector operators

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