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Wigner transform of $O_1 O_2$ in terms of Wigner transforms of $O_1$ and $O_2$?
The Wigner-Weyl transform of a quantum operator $O$ is defined as
$$
W[O](q,p) = 2 \int_{-\infty}^{\infty} dy\ e^{- 2 i p y} \langle q + y | O | q - y \rangle \ dy
$$
and then given a density matrix $\...
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Are Wigner functions of any Unitary operator in $B(L^{2}(\mathbb{R}))$ in $L^{2}(\mathbb{R}^{2})$?
Are Wigner functions of any Unitary operator in $B(L^{2}(\mathbb{R}))$ in $L^{\infty}(\mathbb{R}^{2})$?
i.e.
Let $e^{iA} \in B(L^{2}(\mathbb{R}))$. Define the Wigner function (Wigner transform) as ...
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