For Wigner transforming the function of operators(adsbygoogle = window.adsbygoogle || []).push({}); xand: (pxp+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 tookx=x andp=(h/i)∂/∂x.

I was expecting g(x,p)=xp

Actually I realise 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.

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# Wigner Weyl Transforms

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