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I want to calculate the Wigner quasiprobability distribution function of a particular wavefunction. The definition suggests a few straightforward ways of calculating it, but I was wondering if there's something more efficient than the naive approaches of either directly evaluating the integral or taking the fft of the autocorrelation.

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    $\begingroup$ I have found the integral to be one of the more annoying ones because the integrand is pretty oscillatory. Is this paper helpful? mechatronics.ece.usu.edu/foc/FRFT/references/… $\endgroup$
    – AlexE
    Apr 23 '14 at 7:29
  • $\begingroup$ @AlexE: The paper itself isn't especially helpful, but some of the articles it cites are. In any case, the faster algorithms appear complicated enough that I think I'll start with the naive ones, if only to save on coding time. $\endgroup$
    – Dan
    Apr 23 '14 at 20:56
  • $\begingroup$ Great. Please let us know if you find a good method or good literature. In how many dimensions is your signal/wavefunction defined? $\endgroup$
    – AlexE
    Apr 23 '14 at 20:59
  • $\begingroup$ @AlexE: In this case it's just one. Given the dimensionality of the wigner functions of high-dimensionality wavefunctions, I suspect that most people working on non-1D problems would project to 1D before calculating the Wigner distribution. $\endgroup$
    – Dan
    Apr 23 '14 at 21:45
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    $\begingroup$ That's what I had done, too. It's very common also in classical dynamics, compare mathworld.wolfram.com/SurfaceofSection.html Also consider other phase space distributions, such as Husimi's one: journals.aps.org/prl/abstract/10.1103/PhysRevLett.55.645 $\endgroup$
    – AlexE
    Apr 25 '14 at 7:50

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