# Why does this anticommutator yield this particular result?

1. Sep 25, 2015

### space-time

I was calculating the anticommutator between the momentum operator p and the position operator x (just pretend that p and x have the little operator hats above them). Here is the expression:

{p , x} = px + xp

Now we know that p is as follows:

p = -i(∂/∂x) (Note: I am using natural units so ħ = 1)
x = x

Now, to solve the anti-commutator:

px = -i * [ ∂(xf(x))/∂x] = -if(x) - ix(∂f/∂x)
xp = -ix(∂f/∂x)
px + xp = -if(x) - ix(∂f/∂x) - ix(∂f/∂x) = -if(x) - 2ix(∂f/∂x) = -if(x) + 2xp

Now just take out the f(x) (which was just a place holder function) and you should get:

{p , x} = -i + 2xp

However, some websites that I have gone to in order to check my work suggest that the answer is supposed to be:

i + 2xp (notice that the i has no negative sign).

Why is this? What happens to that -i that is supposed to be there? Did I make a careless mistake anywhere or did the website make a mistake?

2. Sep 25, 2015

### Orodruin

Staff Emeritus
Please link to websites you refer to. Otherwise we have no way of checking what you are referring to.

Regarding your problem, it is much easier to use the relation [A,B] + {A,B} = 2AB, which holds for any operators A and B. You can check your answer using it.

3. Sep 27, 2015

### Haborix

In this link, note the ordering of operators in the final expression of the second answer. I don't know which website you're looking at, but pay attention to the order of operators.