Commutator Relations; Conjugate Product of a Dimensionless Operator

[lukka]

Consider the following commutator for the product of the creation/annihilation operators;

[A*,A] = (2m(h/2∏)ω)^1 [mωx - ip, mωx + ip] = (2m(h/2∏)ω)^1 {m^2ω^2 [x,x] + imω ([x,p] - [p,x]) + [p,p]}

Since we have the identity;

[x,p] = -[p,x]

can one assume that..

[x,p] - [p,x] = [x,p] - (-[x,p]) = -2[p,x]

 

[CompuChip]

That's right.

(And of course [x, x] = [p, p] = 0).

 

[lukka]

Thanks CompuChip