QM: Spin -orbit coupling: Solve [(L.S), L]

[Aaronse_r]

[SOLVED] QM: Spin -orbit coupling: Solve [(L.S), L]

Homework Statement

Griffiths problem 6.16
Solve the following commutators (he lists a bunch but i can't get even the first one)

(a) [(L.S) , L]
(b) [(L.S) , S]
(c) [(L.S) , L^2]

there's a few more, but i think if i get the idea then i can do the rest. I know it isn't supposed to be hard but for some reason i can't get it.

Thank you any help you can give.

 

[Rainbow Child]

The only thing you have to know is the commutators

$$[L_i,L_j]=\epsilon_{ijk}\,L_k \quad [L_i,S_j]=0$$

and the general rule

$$[A\,B,C]=A\,[B,C]+[A,C]\,B$$