- #1
lukka
- 24
- 0
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]
[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]