- #1

kel

- 62

- 0

The questions that I have are:

Prove the following for arbitrary operators A,B and C:

(hint-no tricks, just write them out in full)

i- [A,c1B+c2C] = c1[A,B] + c2[A,C]

So far I've got

A[c1B+c2C] - [c1B+c2C]A = (Ac1B+Ac2C) - (c1BA + c2CA)

giving

Ac1B+Ac2C - c1BA + c2CA = c1[AB] + c2[AC] - c1[BA] + c2[CA]

but I don't know what to do from here - something should cancel, but I think my workings may be wrong.

ii-[A,BC] = [AB]C + B[A,C]

iii-[A,[B,C]] + [B,[C,A]] + [C,[B,A]] = 0

I may be able to do this one based on number ii above, but I need some help on that one first please.

Cheers

Kel