What Are the Commutator Relations Between Hermitean Operators A and B?

[Seanskahn]

hi

I found this in textbook:

[A,B] = [$$\Delta$$A, $$\Delta$$B]

Experimenting witht he expressions of $$\Delta$$A and $$\Delta$$B, I find
[$$\Delta$$A, $$\Delta$$B] = [A,B] - [A, <B>] - [<A>, B] + [<A>,<B>]

A, and B are two hermitean operators, and $$\Delta$$A = A - <A> etc, so <A> and <B> do not commute in general.

What am I missing?

 

[arkajad]

$$\langle A\rangle,\langle B\rangle$$ are real numbers (times the identity operator). They commute with everything.

 

[Seanskahn]

ok, found it

For those who might want to know the answer, <A>, <B> are scalers, not operators, so they commute with each other, and the operators, A and B

 

[arkajad]

Good. So you found it exactly at the same time when I posted my comment.