- #1
space-time
- 218
- 4
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?
{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?