This has to be something stupid which I'm just not seeing. Let with and
Further, let be the multiplication operator on with
can be extended to a unitary operator on
show that the following commutation relation holds
Where denotes the identity function
This is what I have:
but here the commutation relation does not hold. Am I using the definitions wrongly?
So then
and
in which case the commutation relation holds
The only part that is bothering me is the multiplication operator or more generally
The way I have it is that it is defined in the following way
now in the second case we had
so why do we not use the rotated coordinate but just ?