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.