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Why does this anticommutator yield this particular result?

  1. Sep 25, 2015 #1
    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. jcsd
  3. Sep 25, 2015 #2


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    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.
  4. Sep 27, 2015 #3
    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.
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