# Questions tagged [wigner-transform]

The Wigner transform is the bridge between Hilbert space operators to phase-space quantities (c-numbers). Use for issues relating to the Weyl correspondence (the inverse of the Wigner transform), the Wigner function (the Wigner-transform of the density matrix) and, in general, Quantum Mechanics in phase space issues, such as the *-product, the Wigner transform of the operator multiplication operation. May also use for distributions such as the Husimi.

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### Wigner-Weyl transform for a function of coordinates only

I am reading this paper by Tatarskii, which serves as an introduction to the Wigner representation of quantum mechanics. There is a step in the paper involving the Weyl transform that does not seem ...
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### Wigner Function and Spin in the Classical Limit?

This is something I got curious about. Let's say I have the Wigner function for an $n$ particle system: $$W \equiv W(x_1,\dots,x_n,;p_1,\dots,p_n)$$ Now, let's say this system obeys has spin. As far ...
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### Generalization of Wigner overlap formula

I want to generalize the Wigner overlap formula, $Tr( F G ) = 2 \pi \int_{-\infty}^{\infty} dq \int_{-\infty}^{\infty} dq W_F(q,p) W_G(q,p)$, where $W_F(q,p)$ and $W_G(q,p)$ are the Wigner functions ...
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### How does the Weyl transform take into account which quasiprobability distribution was used?

I'm trying to get a better understanding of the Weyl correspondence which, as described e.g. on Wikipedia, gives "an invertible mapping between functions in the quantum phase space formulation ...
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### Time Evolution of Wigner Function

The Wigner Function is defined as: $$W(x,p,t)=\frac{1}{2\pi\hbar}\int dy \rho(x+y/2, x-y/2, t)e^{-ipy/\hbar}\tag{1}$$ Where $\rho(x, y, t)=\langle x|\hat{\rho}|y\rangle$. I am supposed to find the ...
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### What is wrong with Weyl-Wigner representation?

The Weyl-Wigner representation is a useful tool to study QM from a semiclassical, phase-space point of view. My question is simple: if this method is so close to classical mechanics, why don't we use ...
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### Free evolution of a density matrix in position space

I have a density matrix $\rho$ in momentum representation at time $t=0$: \begin{equation} \langle p' |\rho(0) |p\rangle = \sum_{n=1}^{1000} p_n \Psi_n^*(p',0) \Psi_n(p,0) \end{equation} ...