- #1
aim1732
- 430
- 2
For Wigner transforming the function of operators x and p : (xp+px)/2 we need to evaluate something like:
g(x,p) = ∫dy <x - y/2 | (xp+px)/2 | x+y/2> e(ipy/h)
where h is h/2π.
Now I am not sure how to evaluate <x - y/2 | (xp+px)/2 | x+y/2> . I mean what I did was think of |x+y/2> as a delta function whose eigenvalue is x+y/2 and the basis to use is (from the bra) x-y/2.But that gives
∫(xp+px)/2 * δ(-y) e(ipy/h)
which comes out to be a constant where I took x=x and p=(h/i)∂/∂x.
I was expecting g(x,p)=xp
Actually I realize its quite a stupid doubt, rather a problem of me not understanding notations.I would be grateful if somebody gets me out of this mess.
g(x,p) = ∫dy <x - y/2 | (xp+px)/2 | x+y/2> e(ipy/h)
where h is h/2π.
Now I am not sure how to evaluate <x - y/2 | (xp+px)/2 | x+y/2> . I mean what I did was think of |x+y/2> as a delta function whose eigenvalue is x+y/2 and the basis to use is (from the bra) x-y/2.But that gives
∫(xp+px)/2 * δ(-y) e(ipy/h)
which comes out to be a constant where I took x=x and p=(h/i)∂/∂x.
I was expecting g(x,p)=xp
Actually I realize its quite a stupid doubt, rather a problem of me not understanding notations.I would be grateful if somebody gets me out of this mess.