Does an operator X commute with its differential operator?

Question

anonymous · Answer

I mean, I have a problem where there is an operator X = x (the position operator in Quantum Mechanics). Then I have the differential operator Dx. Do they commute?

zzr0ck3r · Answer

operations don't commute with each other.

zzr0ck3r · Answer

unless its an operation on a set of operations.... so I am confused by your question.

anonymous · Answer

@zzr0ck3r Thanks!

zzr0ck3r · Answer

What I am saying is, the question does not make sense. I was not answering "no"

anonymous · Answer

Well, I have to find the value of the commutator of the momentum operator and the Hamiltonian operator. After some substitutions, I got to an expression $$\frac{ d }{ dx }V(x) - V(x)\frac{ d }{ dx }$$ This is what I am referring to.

zzr0ck3r · Answer

Ah so you want to know if that is 0

anonymous · Answer

Yes

zzr0ck3r · Answer

v(x) d/dx = v(x) d/dx(1) = 0.

this is what I see....I am confused by the placement. Maybe @ganeshie8 knows whats going on

anonymous · Answer

Why did you put 1 in the expression?

zzr0ck3r · Answer

To show why I think its weird. You can put 1 next to anything...

ganeshie8 · Answer

this topic is definitely not my level ;-;

anonymous · Answer

Alright, thanks to both of you

zzr0ck3r · Answer

If you don't get any help soon here, I would try http://math.stackexchange.com/

anonymous · Answer

Okay