Thread: Commutators

Calculate the following commutators:
a) [x, i d/dx ]
b) [x, d/dy ]
c) [-d^2/dx^2, x ]

Originally Posted by myoplex11

Calculate the following commutators:
a) [x, i d/dx ]
b) [x, d/dy ]
c) [-d^2/dx^2, x ]

The best way I know to calculate these are to operate on an arbitrary function.

a) for example:


So operate this on some function :



(Remember we need to use the product rule on the last term.)



Thus


Thus


-Dan