Defining Wigner for particle bases

[DhruvaSambrani]

Given a state in the position/momentum bases, we can calulcate the wigner function as (black text)

as defined in wiki.

We should implement this function for states on the particle bases.

[DhruvaSambrani]

A starting point can be

function mywigner(psi)
    map(Iterators.product(samplepoints(psi.basis), samplepoints(MomentumBasis(psi.basis)))) do (x, p)
        xmax = psi.basis.xmax
        xmin = psi.basis.xmin
        N = psi.basis.N
        dy = (xmax - xmin)/N
        getloc(x) = round(Int, (x - xmin)/N) + 1
        ys = collect(filter(y->(xmin<x+y<xmax)&&(xmin<x-y<xmax), samplepoints(psi.basis)))
        1/(π*ħ) * sum(ys, init=0) do y
            conj(psi[getloc(x+y)]) * psi[getloc(x-y)] * cis(2*p*y/ħ) * dy
        end
    end
end

However, a better approach may be to actually perform a FT instead of running a sum

[Krastanov]

Starting with a simple implementation is perfectly reasonable. If you have the time, please submit a PR and the rest of us will try to help with review.