In contrast to classical physics, the language of quantum mechanics involves operators and wave functions (or, more generally, density operators). However, in 1932, Wigner formulated quantum mechanics in terms of a distribution function $W(q,p)$, the marginals of which yield the correct quantum probabilities for $q$ and $p$ separately \cite{wigner}. Its usefulness stems from the fact that it provides a re-expression of quantum mechanics in terms of classical concepts so that quantum mechanical expectation values are now expressed as averages over phase-space distribution functions. In other words, statistical information is transferred from the density operator to a quasi-classical (distribution) function.
CITATION STYLE
O’Connell, R. F. (2009). Wigner Distribution. In Compendium of Quantum Physics (pp. 851–854). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-70626-7_238
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