Do momentum and position commute with potential and Hamiltonian?

[bon]

Homework Statement

See q attached

Homework Equations

The Attempt at a Solution

Am i right in thinking that the answer to both questions is yes? Neither of the commutators [p, V(x)] nor [x, H = + or - ih..

therefore is the answer to both a and b yes?

 

[bon]

The thing is that [p, V(x)] gives -ih/2pi DV/DX where D/Dx is partial d/dx..

does the uncertainty principle only hold between oberservables whose commutator = plus or minus ih /2pi?

Thanks

 

[bon]

Can anyone help with this?