Hamiltonian-momentum commutator

[jarvinen]

I have a potential of -1/r and I need to compute \left[H , \ \mathbf{p} \right].

I got the result of i \hbar \left( \frac{1}{r^{2}}, \ 0 , \ 0 \right).

Am I wrong about this?

 

[dextercioby]

Can you post your method of computing the commutator ?

 

[jarvinen]

Just used that \mathbf{p} = -i \hbar \nabla and H = \frac{- \hbar ^{2}}{2m} \nabla ^{2} + U

Hence H \mathbf{p} \psi - \mathbf{p} H \psi can be written but note that the \mathbf{p} \dot \mathbf{p} part of H will commute with \mathbf{p}, hence only consider U \mathbf{p} \psi - \mathbf{p} U \psi = \left( -i \hbar \right) \left( - \psi \nabla U \right) then substitute for the given U.